Amorgos

This dramatic island is famous for its hiking and diving, fans of the movie The Big Blue (that was shot here) pay pilgrimage to Amorgos.
Make sure you visit the 11th century whitewashed monastery of Hozoviotissa, which clings to the cliffside and is approached by a precarious looking narrow pathway. The sweeping views of the Aegean sea below are well worth the stiff climb.