Any ideas on what we can do during our 6 hour layover at Athens airport--we arrive at 12:50 pm and leave at 7:25 pm for island.
Take the Blue Line Airport Metro into Central Athens for a very quick look around. Target one location and figure out in advance using Google Maps how to get there from either Syntagma Square or Monastiraki Square, both of which are stops on the Blue Line.
I agree with Lee. The metro takes 40 minutes each way and timetables for both directions are at the bottom of this page.
If you go to Monastiraki you will be right under the Acropolis.
I would then turn right out of the metro, in the direction of the Acropolis, and then right again onto Adrianou. You can then walk right round the pedestrianised walk around the Acropolis arriving finally at the Acropolis Museum and metro station. You could then, if time allows, turn left and walk down through Plaka back to Monastiraki. If you find you've run out of time - because you've stopped for a long lunch for example - you can get on the metro at Acropoli and change at Syntagma for the airport.
If that doesn't appeal then I agree again with Lee that one thing is the best, and that really has to be the Acropolis doesn't it? (Unless you've already done it.)