Skiathos is a small island and you can see most of it in 3 or 4 days, so you will have time to island hop in the other two islands, Skopelos and Alonissos.
Skiathos has definitely better beaches from the other two, because they are more organized and it is easy to go. Instead, the beaches of Skopelos and Alonissos are more rocky than sandy and bus timetables are not that frequent or trustful.
Skiathos has great nightlife. I loved the beach bars and the clubs in Kastro. I liked the green and the forests just above the beaches. Koukounaries is surely the best beach to swim, but Ftelia and Agia Paraskevi were also adorable. A boat from the town makes the trip to the north, where you will see some amazing sea caves, the Lalaria. Ferries to Skopelos are very frequent. Both islands are beautiful but different. Skiathos is for fun, Skopelos and Alonissos for relaxing.