As part of Kate's cultural tour of Greece, she and I toured around the archaeological sites in Athens. You can read her account here: Touristy Stuff.
As she noted, the tickets are crassly expensive in the summer, compared to the 12 euros I paid in March. Full price tickets are 30 euros. It's worth it, but it's so crass.
As part of our tour, we went to Hadrian's Library, which I hadn't seen from the inside, and Kerameikos, which I hadn't seen at all. Both were fairly forgettable. You can see similar stuff in other places. I'm sure historians/archaeologists/some Greeks will want to slap me in the face for saying that, but I said it, and I won't take it back. Since you're paying for the ticket, you might as well do a quick pop-through of these places, particularly Hadrian's site, since it's right in the heart of all the other stuff. If you have very limited time, stick to the two good ones--Acropolis and Ancient Agora.
One point about Kerameikos, you can take the blue line metro from Monastiraki (or Syntagma, or wherever the blue line runs) to the Kerameikos stop, but it's still a 5-10 minute walk to the site from the metro, and not very clearly marked. The best way I can describe it is to tell you to walk toward the campus, cross the big street, and turn left along the pedestrian-looking pathway that is actually a road, so don't walk in the middle of it. Or use Google Maps. Here are photos:
|Ancient Athens city wall at Kerameikos.|
|Ancient old stone altar at Kerameikos.|
|Unlabeled old crap at Kerameikos. By the way, Kerameikos is the ancient city of Athens. The city was on the inside, surrounded by a wall, and the cemetery was around the outside. The ancients were surrounded by dead guys.|
|There were ropes blocking off some areas, but not other areas, so we don't know if we were supposed to be in this area, or not.|
|Walking down the ancient road toward the ancient cemetery.|
|More ancient cemetery.|
|Even more ancient etc.|
|Hadrian's library in background, old Roman mosaics in foreground.|