We were in Greece a few years ago, and there was a commuter train that went from the downtown area to Piraeus. I don't know if there is direct bus transportation from the airport to Piraeus. You can probably get that information on the internet as well as costs.
We went to a number of the islands, but we also spent a great deal of time on the mainland. Many stampede to the islands, overlooking the rest of Greece which I think is even more interesting.