The best beach on Amorgos is Agia Anna, a narrow strip of sand and pebble at the base of the cliff directly below the Hozoviotissa monastery — which makes it one of the more dramatic swimming spots in the Cyclades. The water is deep blue, clear, and cold, and on calm days the snorkelling is excellent.
The beach appears in the famous underwater sequence of Luc Besson's film Le Grand Bleu, and for good reason: the underwater landscape here is striking. There is a small bar/café serving cold drinks in summer. Reach it by a steep path from the road above, or by boat from Katapola harbour.