Accommodation in Amorgos
It is easy to find good accommodation on Amorgos, the standard is generally high and the price level is normal. With one exception: if you are going to Amorgos during the high season - mid July to end of August - you should pre-book and be prepared for high prices.
What you always must do, no matter when you arrive, is to pre-decide in which village to stay in: Katapola or Aegiali. Indeed, there are also pensions in Chora, Langada and Tholaria, but usually only the most dedicated enthusiasts stay there overnight.
Personally, I prefer Katapola for the nearness to Chora, Agia Anna and the monastery Hozoviotissa, and for the great advantage of Katapola's location in the middle of the island, it is as far to Aegiali in the northeast as to Arkesini in the southwest. Aegiali suit families with children excellent, thanks to the child-friendly beach. If you have trouble making up your mind, you can stay a few nights in Katapola and some in Aegiali.