If you like the Mediterranean style of cooking, be prepared to have your tastebuds to light up! Greek food in Athens is everywhere, in every form you could think of. From cheap fast food to gourmet delights, Greece has amazing food.
As far as fast food goes, there are McDonald's in Athens. Do not fear, the West has gained somewhat of a threshold! But for every McD's, there is a Goody's and an Everest just around the corner. And those, are far superior to even our standards. Goody's is a typical hamburger joint with pasta dishes on the menu as well. Their hamburgers are amazing and cheap! Everest is exactly what America needs in terms of fast grab-n-go food. They have spanikopita, tiropita, ham and cheese-pita (termed jambon kai tiropita), pizza, and various deserts and sandwiches. They are what I practically lived on as a student during the week! Very yummy and only averaging about 2 Euro per food item.
As far as something more average in price but more upscale than fast food, the Plaka, Monostiraki, and Syntagma are all wonderful in terms of cafes. I highly recommend any of the side street cafes versus the main plaza. They have great owners and are always willing to serve a great meal. If you're in the mood for something that isn't necessarily Greek but still good, try the Hermion. It's right off the main square in the Plaka and has beyond amazing food, for a good price.
A little note about the way food is priced and served to you: Go expecting not to get free anything. You don't typically get bread and butter, like in America, nor are refills free. Water even costs Euros, as the supply of fresh is really hard to come by in Greece. The food is well worth the price, but you're going to want to learn to conserve your drinks while out and about. Another great thing about food service is the fact that you can hang out in cafes all night as long as you buy something. They rarely boot you out, unless you are obnoxiously disturbing or its time to close.