In the Turks and Caicos, a new oceanfront villa at Sailrock Resort (villa from $2,265) fills the bill: it’s a self-contained three-bedroom unit with its own pool, two miles from the island’s other 35 suites and villas. Or opt for Ambergris Cay (doubles from $1,200), a 10-suite, six-villa private-island resort, which has its own airstrip.