I was once walking through the back streets of a tourist neighbourhood when I heard a woman on her cell phone explaining how she had discovered a “secret out of the way" restaurant. Seeing as she was in one of the main tourist areas in Athens, I don't think there was anything secret about her find at all. That's not to say that she was wrong, she just doesn't understand how most Greek restaurants work.
While there are many chain restaurants in Athens, there are far more locally (and sometimes family) owned tavernas (Greek taverns). While they all sell Greek food, many of them have something unique about them. It could be a specialty dish, or just a certain environment. Many offer specialties from areas in Greece but outside of Athens. I have yet to taste a really bad taverna, but I have seen a few very overpriced places.
A good rule to know if you're going to pay too much depends on your proximity to parked tour buses. The further you travel from tourism, the cheaper your meal will. But don’t worry, a cheap meal doesn’t mean you’re getting lesser quality food. If you leave tourist filled neighbourhoods like the Plaka, Thesio, and Kolonaki, you’ll find some great treasures. But you may have some trouble navigating the menus, since many of the smaller tavernas in residential neighbourhoods may not offer English menus.
As an added note, my favourite gyros shop looks like a tourist trap, but it's reasonably priced and fantastic (Thanasis at Monastiraki square).