Tied with Santorini, its more famous neighbor, Anaphi is the south most island of the Cyclades chain ( if you are going to be in Santorini, its only an hour away) and offers an God sent opportunity to get away from the crowds which is something you cannot do in Santorini especially during high season.
Ferry schedules are erratic but well worth it if traditional Greece and fewer crowds are your idea of a what a Greek island should be.
With only 300 residents the islanders are warm and open hearted and sustain themselves primarily with fishing.
Agriculture is difficult due to the soil and many foodstuffs are shipped in from other islands and the mainland causing them to still be cheaper than Santorini where the same applies but without the attitude and hefty mark up.
Replete with a nice hilltop Hora and convenient port just below, the island offers everything one needs (including sandy beaches and fresh seafood) for a great get-a-way from the crowds! Throw in the secluded walks and deserted north side of the island and you've got a small paradise. Bring your sensible shoes and sun hat!