As a recent non-rev visitor to both Athens and Istanbul, I recommend both. But I put IST in first place. Much more to see and do for history buffs, plus the fun of taking a $1 ferry ride from Europe to Asia. You can get a good subway/tram ride from the airport right to Sultanahmed, one of the city's hearts, and the travelers center. Many hostels and cheap but good hotels are to be found there. Also there are the lovely Blue Mosque and Hagia Sofia, one of the major historic buildings of the ancients. It has been in turn a shrine of early Christianity and Orthodoxy and then -- with the coming of the Turks -- a mosque. In the 20th century, Ataturk turned it into a museum to honor all of Turkey's historic influences. An amazing place indeed.

From Athens airport, you can take a bus or train to the heart of the city. To be frank, apart from the historic district of the Plaka and, of course, the buildings of the Acropolis, there's not a lot to see and do in Athens. The food is great, the people are warm; but so is it and are they in Istanbul. A couple of days in Athens is swell -- and then take a subway to Piraeus for a ferry out to one of the islands.

Good traveling.