Interested in historical sites as well as places where you can absorb some Greek culture - places to eat, socialise, events to watch...
I was only there for 2 days a year or so ago during the Champions League Final. Syntagma square is a nice place to hang out and have something to eat / drink (much more so if there aren't 50,000 football fans milling about!) As far as Historical sites you're surrounded by them but you HAVE to see the Acropolis, Theater of Dionysos, and if you can get out to Marathon to see where the biggest Greek battle ever took place and of course where the messenger ran from back to the Acropolis to give news of the victory giving us the modern day name for the long distance race... about 10 years ago
Athens sucks is my personal view!. I love Greek History, but was a little dissapointed in how badly maintainined the Pathenon etc was. 7 days in that place would drive me nuts, aside from the acropolis and the museum there is really not a lot to see. I suggest getting out of there!, head over to the Islands for a while and chill out :-) about 10 years ago