Amorgos (Αμοργός)
Where Luc Besson's film The Big Blue was filmed. Mountainous and rugged with fantastic waymarked walks.
Not very easy to get to but well worth a visit. The famous monastery of Panagia Hozoviotissa is perched precariously on the side of a cliff 300m above the sea. There are two main settlements, at Egiali and Katapola, and ferries often stop at both.