Image copyright Thinkstock Image caption Mesa Verde and the surrounding attractions could fill a week's holiday

US President Barack Obama rattled off a list of iconic US tourist destinations as he launched a campaign to attract more international visitors. But what about the places that could be world-renowned - but aren't?

"When it comes to tourism, we have a great product to sell," said the president, while visiting the Baseball Hall of Fame in Cooperstown, New York, last month.

"Nothing says `Made in America' better than the Empire State Building or the Hoover Dam."

It was part of a pitch for foreign visitors to spend their money on American travel.

But these places are old hat. Five travel experts give their view on the places that aren't on the international tourist map, but should be.

Harrodsburg, Kentucky

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Though founded in England, the Shaker faith left an indelible mark on American culture - from Aaron Copland orchestral suites to an enduring design aesthetic. Known for their simple lifestyle but doomed by their aversion to procreation, the Shakers peaked in the 19th century.

In Harrodsburg, Kentucky, however it is still possible to experience "a retreat into a slower, more reflective way of life", says Patricia Schultz, author of 1,000 Things to See Before You Die. There you'll find the Shaker Village of Pleasant Hill, "one of the few restored Shaker communities where you can stay overnight", she says.

The Shaker Village of Pleasant Hill provides a glimpse into this part of American history, as well as a lot of lovely scenery - rolling hills, horse farms, stone fences and 3,000 acres (1,214 Ha) of beautiful countryside.

Mesa Verde, Colorado

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Colorado has no shortage of natural beauty, from the snow-capped Rockies to its 24 million acres of forests. But in the south-western corner of Colorado, natural beauty, man-made innovation and a unique American history combine at Mesa Verde National Park.

"Thousands of years ago, housing for Native Americans was carved into the side of the mountains," says Kim Mance, editor of GoGalivanting.com. The ancient Pueblos began carving dwellings in the 12th Century, and 200 years later they had established an entire city in the sandstone, including a palace with 150 rooms.

Now tourists can wander through the dwellings on guided tours, or hike, camp or snowshoe through the park. "It's magical," says Mance.

The area is rich with parks, ruins and other destinations: Mesa Verde is also just a short trip away from the Four Corners, where the borders of Colorado, New Mexico, Arizona and Utah converge. Mace also singles out the nearby town of Durango, Colorado, which boasts a mix of modern restaurants and shopping as well as historic attractions like dude ranches and an 1880s-era steam-powered train.

The Finger Lakes, New York

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Though Sonoma County and Napa Valley in California are world-renowned destinations for wine lovers, New York's Finger Lakes region is a must-visit for any oenophile.

"It's an area of gorgeous waterfall filled-hikes, a burgeoning local culinary scene and more than 100 wineries set among two-lane roads, rolling hills and seasonal roadside stands," says Allison Busacca, the editor of BBC Travel.

Busacca says the crowds don't flock to the Finger Lakes the way they do to California wine country. It's also an easy side trip for those hitting the big sites in New York City - it's just four hours north, making it a perfect complement for foreign visitors looking to see a lot of America during a quick trip.

Top Five Most Iconic US Destinations

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As chosen by the readers of USA Today:

Graceland Mount Rushmore National Civil Rights Museum The Grand Canyon Statue of Liberty and Ellis Island

Source: USA Today 10Best

The wine, especially Rieslings and reds, are consistently award-winning, but the prices are low.

"Tasting fees are rarely more than $5, winery owners are easy to find in the tasting room, and hotels and restaurants in the region are often half the price - if not more - than comparable properties and meals in New York City."

Museum of Science and Industry, Chicago

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The entire city of Chicago should be a top destination for anyone visiting the States, says Lonely Planet travel guide writer Karla Zimmerman. She says that the Windy City has restaurants, shows, shopping and culture to match any other US city.

"I'm always surprised when I talk to people who are well travelled, but have never been to Chicago," she says. "They've heard Chicago is cool but never thought it was worth going out of the way for. It's fly-over territory."

Chicago may be more appealing to the foreign traveller now for its association with President Obama, who calls the Hyde Park neighbourhood his home.

Within that neighbourhood is Jackson Park, site of the 1893 World's Fair, which introduced both the Ferris Wheel and moving pictures to the world.

The expo's Palace of Fine Arts is now the city's Museum of Science and Industry, a gorgeous Beaux-Arts building right on Lake Michigan that is now the largest science museum in the Western Hemisphere.

Valley of Fire, Nevada

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In 2013, 40 million people visited Las Vegas. But for the international traveller feeling overwhelmed by all the glitz and gaudiness of the Strip, serenity is just thirty miles north.

"It looks like another planet," says Andy Murdock, managing editor at AirBnB. In fact, scenes from several movies have been shot at Valley of Fire, Nevada's largest state park.

Here, the sparkle is provided by hundreds of thousands of stars, not neon on the Vegas strip, and the skyline is dominated by swirling red sandstone formations instead of giant casinos.

Murdock notes that car rentals in Sin City are usually inexpensive, and a trip to the park can provide a much-needed palate cleanser.