But the payoff of our journey was evident once we set foot on those beaches. Justifiably famous is Playa Flamenco, a curving mile of white sand and turquoise water that draws the biggest crowds and has the only commercial development: a half-dozen kiosks selling mango smoothies, rice-and-beans burritos and all manner of seafood, from conch salad to skewers of shark. One island resident called it “compromised,” since vanloads of day-trippers come over on the ferry, but even Flamenco is unspoiled by East Coast seashore standards.

We tried a new beach, sometimes two, each day. Zoni Beach, on the windy north side, was great for wave-jumping in the white-sand shallows, then retreating to the shade of bushes and small trees to read. Playa Larga, also on the windward side, had bathtub-like sandy depressions in the shallow shelf of an old reef. Tamarindo and Melones had fantastic snorkeling, and we quickly learned the best patches for turtle watching, gazing at the electric blues and yellows of tropical fish, and exploring otherworldly forests of coral resembling giant brains and reindeer antlers. Several shops on the island’s only town (known on maps as Dewey for a long-gone naval commander, a name that appears rarely used) rent snorkel gear and stable ocean kayaks for reasonable rates.

Image Waves roll ashore on Playa Tamarindo. Credit... Christopher Gregory for The New York Times

The hilly terrain offered striking views of the island’s large sheltered bay and the ocean around every turn, flawed only by the dozens of signs that oddly informed us in Spanish that we were entering or leaving the tsunami danger zone. No tsunami has done any damage in Culebra in modern history; it looked as if an enterprising sign-sales­man had captured the government’s attention.

We stopped in at the little Culebra history museum, open only on weekends, and ended up spending well over an hour, watching a documentary in which old-timers recalled the days before electricity, the annual invasions of as many as 7,000 sailors (on an island whose permanent population even today is about 2,000), munitions accidents that maimed and killed islanders, and the successful campaign to oust the Navy. The residual effects persist more than four decades later; while we were there, a Navy team closed Flamenco for a day while it disarmed a bomb that had surfaced from the sand. (Culebra may be the only spot on American territory where the occasional car displays a “Nixon” bumper sticker, in gratitude for President Richard M. Nixon’s decision to end the annual military shelling.)

No one will visit Culebra for the night life, but a half-dozen restaurants scattered around the little town offered excellent seafood and Puerto Rican specialties. Dinghy Dock had tables right on the water, with herds of three-foot tarpon lingering dockside for fish heads tossed from customers, and beautiful fishing bats swooping at the water after dusk. The lobster risotto at El Eden was especially memorable, as was the goat stew at Susie’s. Both were open only a few days a week, and we soon learned to call first. The laid-back Culebra attitude toward commerce was summed up by the sign painted on a gift kiosk that we never saw in operation: “Open some days,” it read, “closed on others.”

On our last day, the wind died down enough to let us paddle rented kayaks a mile or so through choppy seas to Cayo Luis Peña, a hilly little island to the southwest that is part of the wildlife refuge. Following the advice of Ken Ellis of the Culebra Bike Shop, who rents all kinds of other things as well, we checked out the snorkeling in a couple of quiet coves, collected sea glass and hollow coconut shells on the beach, ate a picnic lunch and then crossed back to Culebra, paddling from beach to beach with a couple more snorkeling stops. A final push home into the wind, with big swells crashing against the kayaks’ bows and squalls of wind you could see dappling the water ahead, left us happily worn out. Back at the house, over cold beers on the deck, as the Culebrita lighthouse began to blink in the gathering darkness, we schemed aloud about how soon we might be able to return.