Harbour Island, more than any other Out Island, is where the cognoscenti come to bask in ultraluxurious inns and atmospheric small resorts. Follow the celebrities to $600-a-night cottages with views of the pink-sand beach or ultraelegant rooms in Dunmore Town. Eleuthera offers elegant intimate resorts next to pink- and white-sand beaches happily empty of crowds. Those on tight budgets have a range of friendly, tidy, and affordable inns, a few on the beach, for around $100 a night. For urbanites who want all-out American luxury, there are modern town houses with stainless-steel appliances and granite in the kitchens, and bedrooms for the entire family. Whether you spend a lot or a little, the staff on this friendly island will know your name after a day. Many hotels are closed in September and October.