Michelangelo Antonioni's 1960 film L'Avventura begins with seven friends—a wealthy group of gorgeous, disaffected youth—boating on the Tyrrhenian Sea. Their affluence is visible in their languor, their restlessness expressed in their volatility. At one point they anchor off Lisca Bianca, a tiny islet that emerges like a monolith from the sea. When they discover that one of their party, a young woman, has seemingly vanished into thin air, they scramble up and down the jagged cliffs, playing out small personal dramas as they seek to resolve the larger one. The water crashes against the rocks; the sky opens to possibility. The landscape itself becomes another character—stunning, feisty, mysterious.

This has always been the draw of the islands favored by Italians: extravagant nature with a profound feeling of isolation. There is bustle enough on the mainland, where extravagance of a different sort plays out against the backdrop of crowded cobblestone streets, grandiose exchanges, and an infuriating bureaucracy. When it comes time to leave it all behind, Italians want to feel transported. "That's what we do, especially the rich," a Roman friend told me. "They don't want to go to the beach with others. They want to escape civilization. So they go to these impossible-to-reach places and then they build a palace."

I ventured to the Aeolian paradises—seven UNESCO-protected isles scattered off the northeast coast of Sicily—where Antonioni captured the bewildered anxiety of privilege. These are some of the most secluded islands in the world, requiring arduous plane-car-ferry journeys from almost anywhere in Italy. Unless, that is, you are traveling on a private boat. But even then, capricious weather threatens—Aeolus, for whom the islands are named, is the Greek god of wind. "If the islands say no, you don't go," Beatrice Bulgari, a filmmaker and member of the luxury goods family, told me. These magnificent islands are prized all the more, then, for the difficulty of actually reaching them.

Bulgari, who owns a house on Stromboli, the only Aeolian with an active volcano, travels regularly among all the islands. "I am lucky enough to have seen a lot of beautiful places in the world, but there is something very special about feeling like nothing in the middle of nowhere," she said. Bulgari recently shot a movie, The Lack, on Lisca Bianca, partially in homage to Antonioni. "I remember when I arrived for the first time, at 25 years old, and thought, What do people do here? But this nothing, you come to understand, is everything. You never experience it elsewhere."

SALINA

Courtesy of Caopfaro

I got a sense of what Bulgari was talking about after I arrived on Salina. It is the second-largest of the Aeolian islands, and it used to be called Didyme, the Greek word for twin—a reference to the island's two dormant volcanoes, Monte dei Porri and Monte Fossa delle Felci, which are just under and over 3,000 feet tall, respectively. Whereas Stromboli is defined by its active volcano ("You live with the madman," as Bulgari put it), Salina is the most verdant of the islands, thanks to an unusual combination of freshwater springs and volcanic soil.

The impact, visually and physically, is profound. There is bougainvillea—always bougainvillea—draping the simple stone houses, but these welcome bursts of fuchsia are just the beginning. Strolling the main road to Santa Marina, one of the villages on Salina, I came across poppies, yellow gorse bushes, wild rosemary, prickly pear cactus, and caper bushes. (Here, the caper, grown to full maturity, is called a cucuncio and is closer to a green olive with a stalk.) There is also a salt lake, which, in an ecological collaboration characteristic of the island, was once mined for salt. (Salina means salt mill in Italian.)

"It is a cherished agricultural island," said Alberto Tasca, CEO of Tasca d'Almerita, a top Sicilian family winemaker. He should know: Tasca grew up vacationing on Panarea, another Aeolian island,

and when he and his family were on the boat home they always glimpsed an abundant vineyard on Salina. In 2001 they bought it, and in 2003 they opened the Capofaro Malvasia & Resort, an elegant hotel on the vineyard, from which Salina's own Malvasia sweet wine is produced.

Shaped by volcanic activity thousands of years ago, Salina has dramatic cliffs that rise from the cobalt sea, forming numerous rocky swimming coves. The most famous beach is in Pollara, on the island's west side, where everyone directs you to see the sunset. "It is best there because it is more orange," my taxi driver explained as he rushed to get me to it on time. Scenes from the 1994 movie Il Postino, about Chilean poet Pablo Neruda's fictional friendship with his literary postman, were shot here. The beach has been so heavily visited since then, it is now partly blocked off, but it is possible to reach a peaceful cove and, yes, an excellent sunset view.

Following a seemingly bleak tip, I visited the cimitero in Santa Marina. It is a startlingly moving place, with tiny black-and-white portraits on the graves. Behind it is a small pebble beach—adored by locals and still enough of a secret not to have an official name—with tiny fish darting through crystalline waters.

Steps carved into the rocky coastline lead down to the sea at Pollara. Dallas Stribley/Getty Images

Much attention has been brought to the Aeolian islands by various fashion and art stars who own houses there—Domenico Dolce and Stefano Gabbana, Cindy Sherman (Stromboli); Maurizio Cattelan, the bad boy of the Italian art scene (Filicudi); the prominent art dealer Gérard Faggionato (Panarea)—but Salina has always stayed out of the spotlight. "It is not a place where people show off," Tasca said. "You might see the stars here, but they are quiet. Salina is about simplicity without any status symbols, just going deep into life."

Alessandro Grassi, a publicist based in Milan, argued that all the islands are being remade in this image. "Yes, Madonna went sailing there," he said, "but there is also a new generation that cares about the future. They are thinking about these islands as an ecosystem for wine and food." To that end a powerful group led by British financier and philanthropist Ben Goldsmith formed the Aeolian Islands Preservation Fund last year; the U.K.-based non-profit supports sustainable environmental initiatives on the islands.

On my last day, starting at the 17th-century church Santuario della Madonna del Terzito, I hiked the trail up Monte Fossa—the highest peak in the islands—and picked a bouquet of wildflowers among the eucalyptus and pine trees. Near the top I turned to see the green slope of Monte dei Porri and the tiny islands of Filicudi and Alicudi punctuating the sea below. I'd been there for a few days, but I felt the restoration of a month. I too hoped that Salina, both lavish and humble, would stay this way forever.

Where to stay: Capofaro Malvasia & Resort, with its new chef, Ludovico de Vivo. His caper ice cream sandwich is not to be missed (FROM $187, CAPOFARO.IT). Hotel Signum has a wonderful spa (FROM $167, HOTELSIGNUM.IT). Where to eat: Da Alfredo (011-39-90-984-3075), for granita and a pane cunzato (a Sicilian sandwich) on the waterfront.

PANAREA

Hotel Raya on the island of Panarea. Matthew Hranek/Art + Commerce

From a distance Panarea is a breathtaking bit of boulder, only slightly larger than one square mile, with dramatic striations that resemble elephant skin. It is often described as the "Capri of the Aeolian islands," a wealthy retreat with a chic summer scene.

Kate Moss and Uma Thurman have lounged on the terrace of the famed Hotel Raya, a stylish place that opened in the 1960s complete with a seaside disco that instantly put Panarea on every international jetsetter's map. "In July and August it's like a camp for beautiful young people," said Bulgari, whose own 17-year-old daughter has spent many a night dancing at the Raya. But regulars take pains to renounce its party reputation, usually by invoking its past. "When I started going, there was no electricity and no running water," said Antonio Monfreda, an Italian creative director who has been visiting the island since his parents bought a house there in the 1970s. "Star watching and volcano watching"—there is a terrific view of Stromboli smoking a few miles away—"were the great activities."

These days Panarea appeals to the Janus in people—two faces looking in opposite directions—in that you can be seen and you can hide. "It is Capri as I imagine it in the last century," Monfreda added. "When the sun goes to sleep behind you and shines on the rocks, they change from intense yellow to green to violet. And the tiny stone beaches are enchant- ing." The most magnificent of these is Cala Junco, in the southernmost part of the island. High cliffs of basalt tower over water that shifts between turquoise and green. Here, the lure of revelry and fame fades away, and you are returned to a primitive solitude.

Panarea's Casa Visconti. Oberto Gili

Though some despair that the Hotel Raya brought nonstop rollicking nightlife to the island, the owners, Myriam Beltrami and Paolo Tilche, brought a sophisticated aesthetic, too. The hotel is a sprawling event, rambling up a hill from the port on the east side of the island; the architecture is Greek-influenced, and the impeccable interior design has an Indonesian inflection. (Beltrami spends part of the year in Bali.) There is a similar Grecian style to Panarea in general. The houses are whitewashed, with the occasional pop of a blue shutter or a green door. The labyrinthine streets winding through the center are without cars or lamps. The days of no electricity may be over, but the preferred method of lighting at night is a Moroccan lantern—or, better yet, a full moon.

Where to stay: Hotel Raya is a must if you want to experience the island in full. The jacuzzi, which uses water from natural hot springs, is rumored to cure ills ranging from arthritis to insomnia (FROM $167, HOTELRAYA.IT). Where to eat: Bridge Sushi is where the elite meet before heading to the Raya to dance. It opens for the season in early June (BRIDGEPANAREA.COM).

FAVIGNANA

The town of Punta Longa. Marka/UIG/Getty Images

Each of the Aeolians inspires a fierce loyalty, but Favignana, the largest of the Egadi islands—a small archipelago off the west coast of Sicily—elicits perhaps the most intense passion among its enchanted inhabitants. The allure of "my Favignana," as it was tattooed on the chest of my boat driver, is undeniably casual and offbeat. There are no luxury hotels here. Italians leave their precious cars behind in favor of biking. And the living is slow. The crudo tastes so fresh it's as if the waiter had simply dipped a plate into the sea; the rocky path to the crescent beach of Cala Azzurra winds past a field of donkeys; and the local museum has no guides—but you'll find your way around just fine.

Ginevra La Cavera, who grew up living part-time in Favignana and now owns Dimora dell'Olivastro, an exquisite B&B on the island, told me that tourists have been coming for less than 10 years. "But there are more coming. From around Italy, of course, but also from Northern Europe, England, and France, even some Americans." Indeed, in the small main village, where the east and west sides of Favignana meet in a slender middle—the island is shaped like a butterfly—a stylish mix of people gather nightly. Giorgio Armani now visits on his megayacht (once accidentally slamming into the pier); Miuccia Prada and her husband Patrizio Bertelli have reportedly bought a seaside villa.

All of them are attracted by the island's intense beauty. "Favignana is wild," my Italian friends say. Part of that wildness comes from its brutal history. On the western side of the island, on a hill called Monte Santa Caterina, sits the Castello di Santa Caterina, originally built as a watchtower for pirates. The island, in fact, spent centuries under attack—by Carthaginians, Romans, Arabs, and Normans. Favignana's most beautiful spot, Cala Rossa (which roughly means "red cove"), got its name from the blood of the dead Phoenicians who washed ashore during the Punic Wars.

Ricci di mare (sea urchin), a favorite local dish. Andrea Wyner

And then there's La Mattanza, the annual slaughter of bluefin tuna that took place for centuries. Until about a decade ago unsuspecting tuna would pass through these waters on their way to the Atlantic. A team of men would wrestle the giant fish, which weighed as much as 1,000 pounds, from the sea and

repeatedly plunge their harpoons into their flesh. Finally, after a run on bluefin tuna—one fetched more than a million dollars on the Tokyo market in 2013—there weren't enough left to continue the event. But La Mattanza lives on in memory, depicted in the stained glass window of the church and in a dignified museum near the port.

Some have heralded Favignana as the next Italian hot spot, but it's unlikely the island will budge for the whims of luxury. The locals understand that the attraction, even for the very rich, is nature and simplicity: the pastures with cows and sheep, the groves of olive and sweet fig trees, the rocky beaches, the grottos that dot the perimeter of the island. When I dove into the water near Cala Rotonda, an exquisite beach on the west side, I found myself swimming into a cave where an opening had formed in the rock ceiling and the sun shone through in a single pillar of light. It was as striking as the beam that pierces the Pantheon, but, like so much of Favignana, it had occurred by the happenstance of nature.

Where to stay: I Pretti, near the center, has a lovely inner courtyard (FROM $164, IPRETTIRESORT.IT). In addition to the elegant B&B Dimora dell'Olivastro (FROM $200, DIMORADELLOLIVASTRO.IT), Ginevra La Cavera plans to open another hotel this year, Dimora Cala del Pozzo, a restored seaside farmhouse (DIMORACALADELPOZZO.IT). Where to eat: Quello che C'e C'e is short on atmosphere but long on crudo—the best meal to be had on the island (011-39-338-609-3149). The wine bar and restaurant Camarillo Brillo (CARMARILLOBRILLO.IT) is the choice of hip Europeans. Side trip: Either of the other two Egadi islands is worth a visit. Marettimo offers a glimpse of life without any pretensions; Levanzo is known for the Grotta del Genovese, home to Stone Age cave paintings. Daily trips are available from mid-June to mid-September.

MADDALENA ARCHIPELAGO

The town of La Maddalena. Montanari/De Agostini/Getty Images

Much attention has been paid to the Costa Smeralda (or Emerald Coast), the 35-mile stretch of shoreline on the northeastern tip of Sardinia, Italy's second-largest island (after Sicily). The Aga Khan created this opulent getaway when he and his consortium bought more than 12,000 acres of coastal property and developed it in the early 1960s.

Soon luxury resorts, golf courses, and former Italian prime minister Silvio Berlusconi (and his notorious "bunga bunga" parties) followed. Many Italians feel this area is now overrun—congested with expensive boutiques and the yachts of Russian oligarch—and have taken to the more secluded Maddalena archipelago, seven islands and many tiny isolotti found in the Strait of Bonifacio, between Sardinia and Corsica.

The largest is La Maddalena, just a mile off the northeastern shore of Sardinia. For 36 years, until 2008, there was a U.S. naval base here, and a NATO base on nearby Santo Stefano. This provided the island with such a strong economy—because the bases hired locals and imported Americans to do business with them— that courting tourism was unnecessary. That's changing, thanks to the closing of the base, as well as the defection of those fed up with the Emerald Coast.

The town of La Maddalena is still catching up to this new surge of visitors; the pastel buildings and central village are sweet and provincial. But never mind: What mattered—what everyone advised—was that I get out to sea. After all, the archipelago shares the same gorgeously clear water and sculptural granite coastlines that first drew the Aga Khan to the Emerald Coast. The only difference is that this area is still untapped.

All I needed was a gommone. Literally that means a rubber dinghy, but in reality there are all manner of boats to be rented in the main port of La Maddalena. (Be sure to book a private tour, not a group outing, as it's best to chart your own course. Elena Tours was very good: ELENATOURNAVIGAZIONI.COM.) Out on the water I discovered a different world. "You can dive into a sea that has nothing to envy the Caribbean," one friend described it, rather poetically.

The other six islands, in descending size order, are Caprera, Spargi, Santo Stefano, Santa Maria (where Oscar-winning filmmaker Roberto Benigni owns a summer house), Budelli, and Razzoli. You can easily visit them all by boat—nothing is more than 20 minutes away, though the ride, while always exhilarating, can sometimes be choppy. "North of Sardinia has the most beautiful and fast-changing winds," a friend who has come here since child- hood told me. "It is never boring sailing here."

Caprera was once largely owned by Giuseppe Garibaldi, one of modern Italy's founding fathers; his home is now a museum. The island also features Cala Coticcio, a beach that has drawn comparisons to Tahiti for so long that it has been labeled as such on local maps. (It is set on two secluded coves and is reached only by a strenuous hike.) The delicate pink rock that surrounds the turquoise water has been shaped by the wind into recognizable forms: a cow, a witch's nose, a reclining woman. Budelli, which was the setting for another Antonioni movie, 1964's Il Deserto Rosso, includes Spiaggia Rosa (named for its unique pink sand). It is now off limits to visitors, but you can still glimpse its blush from a boat.

A secluded spot on the island of La Maddalena. Deagostini/Getty Images

On uninhabited Spargi there are even more remarkable stretches of beach, Cala Soraya and Granara among them. The scene was busier here, with boats all around—yachts, gommoni, sailboats—creating a seaside camaraderie as people plunged into the water, swimming around the pink-gray rock formations and making their way to the silky beaches.

At the end of the day, as we headed back to La Maddalena, we came to Porto Massimo, near the northern tip of the island. It was unexpectedly empty—just the water, the white beach, and me. I dove in and felt a lightness I have experienced only here; the salt- water gives a stronger sense of buoyancy. I drifted, looking up at the broad sky, enveloped by rock and sea, and I felt I had arrived at the edge of the world. Or, rather, that I had arrived at the nothing that means everything.

Where to stay: La Maddalena is underwhelming when it comes to hotels, but Grand Hotel Ma & Ma Resort offers contemporary luxury accommodations, along with a spa and glittering lounge bar (FROM $216, GRANDHOTELMAEMA.COM). Where to eat: La Scogliera, overlooking the water in secluded Porto Massimo, is a must—and so are reservations (011-39-789-187-6556). The charming La Locanda del Mirto, in the mountains, opens on all sides to stunning views (011-39-789-739-056).

Getting there: The perfect times to go to avoid the crowds are late May to early June or the month of September. Boats to Salina and Panarea leave regularly from the Sicilian port of Milazzo, and starting in June there will be hydrofoils (SNAV.IT) from Naples and Palermo. Air Panarea (AIRPANAREA.COM) offers helicopter service from the Palermo and Naples airports. For Favignana, boats depart from the port of Trapani. (Absolute Sicilia is a terrific company specializing in luxury travel within Sicily; ask for Alexandra Buzzi; ABSOLUTESICILIA.COM). Several ferry companies regularly travel to La Maddalena from the Sardinian port of Palau; it takes just 15 minutes.