Omonioa Square has a reputation for being down at the heels, but there are gems to be found there, and in general life there is more authentically Greek than at Syntagma. Papanikolas is part of that--unpretentious all-vegetarian food served cafeteria style by friendly ladies who speak a little English. The price is half what you'll pay at Avocado, Athens' other (and better known) veg eatery, but the food is delicious. You point at one of three or four main dishes, they pile it on your plate, you choose a fresh salad or some fresh bread, get your water and you're good to go. The cafeteria has two levels and upstairs is mercifully quiet and peaceful. If you're addicted to checking your email, this is not the place for you; it's WIFI free. The sign is only in Greek, so brush up on your Greek letters!
Cons: Variety is limited