Being ill, I didn't have my "try everything" appetite but still managed to eat countless $1.30 souvlaki pita gyros, and baklavas, other sweet/assorted goodies sold by street vendors everywhere. If you're looking to trim "fat" from your travel budget, eating/snacking like this was a great way.
Two Plaka restaurants worth mentioning/checking out are O DAMIGOS at Kydathinanion 41 and TO GERANI at Tripodon 14. Both were moderate priced establishments serving typical Greek foods; a full meal costing $12-$17. O Damigos is a basement tavern with checkered tablecloths, an old guy with a hand-accordian in the corner, and excellent seafoods. (I had the swordfish and calamari though salted codfish is the house specialty.) O Damigos is more for locals while To Gerani seemed to draw more tourists. Waiters don't bring menus, but a tray with a little of everything they're serving for the night. Simply see, point and smile. I recommend the house specialty of sausages flambeed in Ouzo...and, not to strike a match until your mouth's cooled off!
Greeks tend to dine after 9:00 p.m. so if you're American and used to eating earlier, getting a table without a reservation should be no problem. Be aware of restaurant employees standing in front of cafes. Simply making eye contact is all but agreeing to dine with them. If you don't, they can be rude and even agressive by your snub.
If you're in the Piraues area, there's a place on the eastern side of centrally located Plateia Karaiskaki I took to calling "Crusty Farts Diner" simply by the old codgers the joint was always full of...so you know the food was authentic and cheap! I ate my fill both times I was in the area, but couldn't really tell you what of. Food was laid out on trays in the window/serving counter...give it the old point and smile! Portions were huge; I never paid more than $7.
Athen's is the only place I've hit fast-food places cause they had reasonably priced "help yourself" salad bars that had interesting Greek salads, veggies and other dishes.
The Cental Market area, Athen's largest, is located on "Athinas" between Sofokleous/Evripidou. The meats area is especially interesting; impeccably sanitary considering they slaughter right there on the sidewalk! Best buys were the salamis, pepperonis and sausages to gnaw on.