The 13-acre Dolphin Island is the domain of Alex Van Heeren, who also owns New Zealand’s lavish Huka Lodge. The rustic-chic Fijian hideaway can host only a single party of up to four people at a time. These lucky few have full command of the frangipani-and-jacaranda–shaded main bungalow, with a wraparound veranda and downy sofas. The air-conditioned, two-bedroom sleeping pavilion is decorated with a collection of South Seas artifacts and a black-and-brown tapa (cloth made from mulberry bark) mural above the bed. Paddle a kayak around the bay or hike across the island’s steep side to a bluff above Bligh Water. There, a coconut-frond hut has a fan-cooled daybed for whiling away the day in seclusion. Back at the resort, the doting staff prepares coconut shrimp, handmade rotis, and mud crab in fresh coconut-cream curry for dinner.