Astypalea is a small island with one of the most beautiful Chora's in the Aegean. The area around Chora is where most people stay with some very nice accommodations and a nearby beach.
However, there's really not a whole lot to do on the island unless you like to just chill out, hit the beaches, hike, walk and soak in a more traditional and untouristy Greek Island.
We were there in October, the weather was lovely, the Aegean warm and almost devoid of tourists, which is what we like.
You didn't mention when you'll be going . . . high season will have most everything open and a bit more lively . . . off season will be very quiet, more authentic, and very Greek.
You may want to check out my Astypalea Trip report here (https://www.tripadvisor.com/ShowTopic-g189437-i17059-k8957510-Astypalea_Trip_Report-Astipalea_Dodecanese_South_Aegean.html)
and a video of my time there here: https://www.tripadvisor.com/ShowTopic-g189437-i17059-k10766753-Astypalea_Videos-Astipalea_Dodecanese_South_Aegean.html
We loved our time on the island but we don't go to a Greek Island to party, shop, nightlife or lay around on a beach, we want Greek culture, tradition, history and especially Greek Food!
If you feel Astypalea meets your needs then I highly recommend it!