3 days in Greece

I would stick to the mainland, rather than adding the vagaries of island ferry schedules (the most changeable type of transportation) in such a short time. See sightseeing notes for the Peloponnese, Dephi, and Athens at http://www.ricksteves.com/europe/greece and fleshed out in Rick's guidebook. If possible, fly from Athens to your next destination (Rome, Germany, home, etc.) to save time. Heck, fly both ways, if Bari is not really central to your Italian travels; see www.skyscanner.com.

Three days is not enough to get to rambunctious about what to see. One day in Athens is only a tease . . . you could spend several days there and still not see enough. However, if you insist on one day in Athens then I would suggest an island like Aegina or Hydra, both very close and short ferry/boat rides. Aegina is one of the nicest islands with a superb ancient temple, an abandoned Byzantine village, centuries old olive trees, is the Pistachio Captiol of Greece, nice fishing village of Perdika and so many other sites that most people don't know about. Hydra has one of Greece's most beautiful waterfronts and a lovely town up and away from the harbor. The best thing about Hydra is that no motor vehicles are allowed . . . all transportation is by donkey! This will give you a taste of the Old Greece. However, Hydra is popular with jet-setters so don't expect old ladies in black and men herding goats/sheep. It's still a favorite for many Athenians!

Thank you for the suggestions and information. Very helpful!

I googled "train from Patras to athen" and it said 3.5 hours.
that's half a day EACH WAY.
I'd check our Ryan Air first but, in lieu of that, choose one small area and stick to it.
Athens is probably the right answer for a first time visit.
I've also been to Corinth, Nafpoli, Epidauros, Mycenae and they are a nice small cluster. But if you see them and not Athens you will feel like you missed the key.