Paros and Naxos are your easy choices. You can checkout the timetables online with Blue Star Ferries. Santorini to Naxos takes around 2 hours, and Naxos to Paros 45 mins (these are not your only choices, and you can go direct Santorini to Paros). You might want to Google hydrofoil too.
For ideas/a browse
http://www.greecelogue.com/ferries-from-santorini-to-naxos-and-return.html

Santorini's ferry port at Athinios is maybe 3-4 miles from Fira (Thira), and there are buses to the port from Fira (and busses from Kamari to Fira).

We did exactly this last year. The inter-island ferries use the port at Athinios a few miles south of Fira. As mentioned Naxos & Paros are well served and from these islands we visited Mykonos, Delos & Antiparos. For a day trip many excursions visit the volcano and then head to Thirasia for a couple of hours for lunch. Not sure if you intend to return from Santorini, we flew back from Athens after leaving Paros on the Blue Star ferry to Piraeus. Its a lovely modern ferry and the 4 hour trip was a great way to end the holiday