Another wonderful sight is the Agora but this is really only for Greek-history-interested people. Otherwise it's hard to imagine what was there!
I also really liked the 3 hills, called 'Pnyx', 'Philopappos' and 'Areopag'. You can walk up to them which is really nice. Nice for walks, to get a few from the town and it's also relaxing. So, after a long day walking around in the tourist crowed it's really good to spend some time there!
And on the way up to the acropolis you are walking through an area with lots of nice restaurants and bars. You should get there some Tzaziki and drink Retsina!
Also nice to get something about Greek history is the national museum.

