It all depends what you like to do. If you're itching to lie on a beach, why not island hop? There are a number of amazing islands to hit such as Mykonos, Santorini, Crete, Kos, Rhodes -- the list goes on and on. If you feel like partying, then check out Mykonos and Santorini. But if you're more into relaxing and getting away from the crowds, try Crete or Kos (islands farther away from mainland tend to be quieter).
There are loads of sights and activities on the mainland as well. Don't miss out on the Parthenon and the Acropolis. you'll start to understand why your history teacher spent so much time on the Greeks. There's also The Temple of Poseidon, which is a nice day trip out of Athens, the National Archeological Museum, Monastiraki, the ancient Agora, and Syntagma to check out. Need to check ferry fares and times? Look no further than www.greekferries.gr.