Kythnos is a low-key island in the western Cyclades, popular with Greek families who come for its authentic character, its beaches and the thermal springs at Loutra. Most of its visitors arrive and leave by sea, and this crossing is the direct link back to the capital, taking as little as an hour and a half on the fast boat.
You have two ports to choose from on the Attica side. Lavrio, south-east of Athens, is closer to Kythnos and serves Kea and the western islands, while Piraeus, Athens' main port, is the better choice if you are heading into the city centre, since metro Line 1 and the tram both reach the port. Compare the two before you book.
Kythnos to Piraeus is served by three companies with very different boats. Seajets runs high-speed craft in the warmer months that do the trip in about 1 hr 30 min to 1 hr 35 min, from €49.70. Aegean Sea Lines and Fast Ferries run slower conventional ferries that carry cars and take around three hours, with fares from €27 and €31 respectively in Ferryhopper's table.
The one thing to watch is frequency. The route is listed all year, but on some weeks there is only a single sailing, so check which days your boat runs before you fix the end of your stay.