My wife and I took the Treasures Tour in May, 2010 with OAT and it was absolutely marvelous. Having been to Athens several times many years before (lived on Cyprus, short hop) I was happy to do only a "drive by" and a short walk around the Parthenon base area. The trade off was more time on the incredibly neat and fun OAT small ship, cruising and visiting the small greek islands, and in the Greek countryside. Athens, IMO, has little to enjoy except for the most famous monuments, and they are undergoing a lot of restoration. The city is pretty unattractive overall, has not grown or been planned well, and is the center of much of the political unrest going on regarding financial woes. During our day in Athens there was a lot of "aftermath" because of a drive by automatic weapons/bombing event that killed several people and wounded others a couple of days prior. Certainly the Parthenon and the National Museum are worth visiting if you could, but Athens itself today is not attractive, at all. It used to be, but time has not been a friend. When we docked our OAT ship in Athens the port workers were holding a "slow down" strike, so we had to float around offshore to await the end of their gesture of defiance toward's cuts in benefits. Politics aside, it becomes a pain for a visitor.
Compare Istanbul to Athens (lived near Istanbul 40 years ago, also visited on the same 2010 tour) and the story is different. Both cities are noisy and the traffic is nuts by American standards, but while the Greek people have always been welcoming in the past to me right now they are pretty glum, especially in the big cities, although the small island and rural residents are their usual wonderful selves. Istanbul today, and the Turkish people overall, is economically booming and welcoming to outsiders, as well as being positive in general. Forty years ago Turks were curious and carefully friendly, but not so used to visitors. Today tourism is booming, and it is a different place, but of course is still Middle Eastern. Istanbul could easily consume a week, maybe more, and you would not be bored or see the same things. More time there, or in Turkey in general, is much more valuable as an addition than more time in Athens.
Sorry you won't get to see what you want, but what you will see you will like, I promise you.