ANGUILLA, British West Indies — I am in shellfish heaven. A super-size platter of Caribbean lobster and Anguillian crayfish sits before me, grilled and spiced to perfection with a secret sauce.Sandra Wallace, co-owner and proprietor of Scilly Cay, a small restaurant off Anguilla’s north coast, reveals the ingredients — orange marmalade, roasted peanuts, curry, tarragon, Dijon mustard, orange juice, honey and olive oil — but not the measurements. After devouring the delicately sweet meat, I settle back with another Ting, the grapefruit-flavored soft drink. My travel companions let me know I’m missing out on the very strong rum punches served up by Sandra’s husband, Eudoxie, known to most as “Gorgeous.”He loves to tell visitors, “Two of those will make you walk on water.”I think I’ll pass. Sandra, a Georgia native, met and married her Anguillian husband while both were living in Atlanta.“After our son was born, we came to visit Eudoxie’s family,” she said. “We decided to stay when we learned that island officials had chosen to go with high-end rather than mass tourism, which ensured that the island would not have neon signs, billboards, time shares, casinos, massive cruise ships or fast-food restaurants. It seemed like a good place to raise a family.” In 1985, they purchased a 2-acre strip of sand, and Scilly Cay (pronounced “silly key”) opened the following year, complete with a spot for helicopter arrivals from St. Maarten. It has developed over the years into a lobster lover’s lunch spot for regular folks and celebrities. Sandra Bullock rented out Scilly Cay for a birthday party, as did Robert De Niro a few years back, for 40 friends, including Robin Williams. Usher, Billy Crystal, Liam Neeson and celebrity couple Sarah Jessica Parker and Matthew Broderick have all chowed down on lobster and crayfish here, not to mention Brad Pitt and Jennifer Aniston, who spent their last vacation together on Anguilla before their famous split. To get there, make your way to the Island Harbor dock just off the north coast, park near the Scilly Cay sign and wave your arms. (You’ll feel silly, no pun intended, but it works!) A boat will soon arrive for the three-minute ride to the island, which is decorated with thatched tiki huts and walls embedded with hundreds of conch shells. Except for special events, Scilly Cay is open for lunch on Wednesdays and Sundays only, so plan accordingly.Arrive hungryAlthough not quite the well-kept secret it was 20 years ago, Anguilla (rhymes with vanilla) remains a low-key destination compared with other Caribbean vacation spots. In 2012, Anguilla’s stay-over arrivals numbered near 65,000; an equal number were day-trippers arriving by ferry. Contrast those numbers with those of its nearest neighbor. St. Maarten/St. Martin, the half-Dutch, half-French island less than 10 miles away, recorded nearly 457,000 stay-over guests last year and 1.75 million visitors arriving by cruise ship.Anguilla is ringed by 33 unspoiled white sand beaches fronting the Caribbean’s multi-hued blue waters. There are a handful of upscale resorts and an increasing number of mega-luxury villas, sought out by A-listers and well-known figures from the world of entertainment, sports and politics. But there are plenty of less pricey accommodations, though with fewer amenities, located on beaches just as stunning. The island boasts more than 100 restaurants, from upscale gourmet dining spots to barefoot casual beach bars, including those located on offshore islands like Sandy Island, Prickly Pear Cay and Scilly Cay. With only about 13,000 residents, Anguilla is similar to a big small town with enough dining choices to try a new place every week for two years. My own introduction to Anguilla dates to 2000, when I read Melinda and Robert Blanchard’s A Trip to the Beach: Living on Island Time in the Caribbean. It is the couple’s story of leaving their home state of Vermont to build a small restaurant in Anguilla. A year after opening Blanchards in 1994, the restaurant was destroyed when Hurricane Luis devastated the island. Blanchards reopened and has become an island institution, hailed as one of the Caribbean’s best restaurants. Most popular is the fixed-price menu, with three choices offered for each course, including several of the restaurant’s signature dishes. It’s a bargain, relatively speaking, at $48 per person. In late 2011, Blanchards opened Beach Shack next to the main restaurant for lunch and dinner in a more casual setting.Beaches and nightlifeThe closest you’ll find to a crowded beach is at Sandy Ground, where boats and yachts from around the world are docked. It’s also the spot to watch boat races during Carnival, held the first week in August, and at other times throughout the spring and summer. Boat racing, a tradition dating to the early 1900s, is considered Anguilla’s national sport.Just when you think you’ve found your favorite strand of sand, you’ll find another that’s just as inviting, like Cove Bay, a long stretch of nearly deserted beach with calm, crystalline waters where we stopped for lunch at Smokey’s at the Cove. Located beachside on Crocus Bay is da’Vida Restaurant and Bayside Grill, where the menu tempts with intriguing items like shrimp pizza topped with Caesar salad. Nightlife on Anguilla, albeit a bit subdued, isn’t nonexistent; you just have to know where to find your musical match. Lovers of reggae music will want to spend an evening at the Dune Preserve restaurant and beach bar, situated on Rendezvous Bay near the CuisinArt Resort, where the island’s most famous reggae entertainer, Bankie Banx, performs four days a week. The Pumphouse in Sandy Ground Village and Elvis’ Beach Bar next door are also among Anguilla’s best places to party and mingle with locals, tourists and the occasional celebrity.Thursday night at Anacaona Hotel’s Firefly Restaurant is not to be missed for those who would like to experience a bit of Anguilla’s culture. Come for the Caribbean buffet and stay for a musical floor show performed by the local Mayoumba folklore troupe. A favorite spot to watch the sun slip into the sea with appetizers and drinks before dinner at Coba or another nearby restaurant is the Sunset Lounge at the Viceroy hotel, straddling Barnes Bay and Meads Bay.Sunday is perhaps the biggest day on Anguilla for local entertainment.Everywhere you go, you’re likely to find people sand mashing, the local term for dancing to the music Anguilla-style. Even Scilly Cay gets into the act, inviting local reggae bands to perform. Have two of Eudoxie’s rum punches, then try walking on water. Or, just take a swim.