Anywhere you go in Greece, apart from the tavernas and the grill houses, one can find the "ouzeri". These places get their name from the popular drink "ouzo", of course. If you don't like ouzo, you can always drink beer or some white wine, I don't recommend it though.
Ouzo is always accompanied by a variety of "meze", meaning appetizers, but you can eat all you want from these appetizers cause their is no main course. This is the fun part... you all eat and try from everything! Small --or not so small-- portions of fried or grilled cheese, small fry (fish), stuffed vine leaves, garlic sauce, meatballs, and plenty of seafood, which is actually a must. Shrimp, shells of all kind, mussels, octopus... you name it! And some nice ouzo to wash everything down!
If you ask me what kind of ouzo should you prefer, I recommend "MINI" or "Plomari". I am a visual type and both of these brands have very interesting bottles apart from being really good ouzos.
As for a recommendation about a place, I will say the same that applies to all types of restaurants: stay away from the obvious touristy ones... prefer the one that gathers more greeks. Unfortunately Plaka is not famous for its ouzeries. Actually, "Sholarheio" is VERY popular but also VERY bad! What can I say? My standards are too high! I prefer one that is not downtown and is called "Psarioti". A really great experience for your taste buds!
Favorite Dish: Lobster spaghetti, small fish soup, grilled octopus, small fry (atherina fish), small fish marinated in vinegar. If you don't like seafood, their grilled meat is fantastic.