desert island

Short definition from Wiktionary

Noun

1. 1
   A deserted island, an uninhabited island, especially one in the tropics and (now frequently misunderstood as) a small and almost entirely sandy desert.
2. 2
   An island that is completely or mostly a desert, an arid island.
3. 3
   Describing a thing considered so personally indispensable or beloved that one could never tire of it, used especially for books and music.