Frenchmans Hotel, Tortola, British Virgin Islands. It's a small (9 units) villa resort near Tortola's West End. It is within short driving distance of other beaches if you wish to explore, five minutes away from the marina at Soper's Hole, from which you can catch a day trip to one of the many other islands in the archipelago.
Although the resort is small, there is a restaurant on the property serving breakfast daily (included in cottage rate), Sunday brunch, happy hour and dinner Tuesday through Saturday. Each cottage has a kitchen and there are grocery stores nearby, giving you options for meals. There are also a number of restaurants within a 5-10 minute drive.