Things to do in Kythnos are limited, as the island is not touristy developed. Kythnos is mostly visited for a short stay before hopping to other islands of the Cyclades or for a summer weekend break for Athenians. Swimming is the only activity to do on the island and in fact most beaches are not organized, therefore you will enjoy privacy.
If you like hiking, this can be a fun activity on Kythnos island in spring and autumn, when the weather is not very hot. Hiking trails are usually not signposted, but they are easy to follow. A nice hiking trail is from the port to Chora or Driopida, the two main villages of Kythnos, or from the port to the lovely beach of Kolona.