It's not deserted, but with only 300 inhabitants it is pretty sparsely populated, and after a couple of days you will have seen everyone on the island.
Less than a mile from the coast of Turkey, Kastellorizo (officially named Megisti) is Greece's easternmost island, and nicely off the beaten track. For fresh home-cooked eastern Mediterranean food try the Olive Garden, in the island's tiny harbour.
A number of boats plough back and forth between Kastellorizo and Kaş, one of Turkey's prettiest fishing towns.
Six flights a week from Rhodes. Several ferries from Rhodes, including a weekly catamaran.
One hour boat ride from Kaş in Turkey.
Google map: bit.ly/xxbntP