Palm Island, St Vincent and the Grenadines It’s hard to imagine a greater luxury than having your own beach-filled private island in the heart of the Grenadines. For many, Palm Island is the ultimate expression of the Caribbean fantasy: just you and the beach, an island in the sun, channeling Robinson Crusoe. But there’s nothing castaway about the experience here, where outstanding food and drink abound and every day is its own water-filled adventure, from snorkeling to, well, afternoon tea.