The waterfront tavernas facing the port in Aegina town are convenient but tend to be priced for tourists and staffed by people whose main skill is catching passers-by. Walk one or two streets back from the water and the picture changes considerably.
For grilled fish and mezedes in a neighbourhood setting, the side streets around the central square and the fish market are the place to look. Lunch service typically runs from 1pm to 4pm, and the best spots fill quickly on weekends. Coming midweek, or arriving at opening time, gives you the most choice. If you see a menu with photos laminated in plastic, keep walking; if you see a handwritten specials board and locals at the tables, you are in the right place.
Aegina is particularly good for octopus — you will see it drying on lines outside tavernas — and for fried anchovies in season. The island also has a small but confident street food culture: pies (spanakopita, tiropita) from the bakeries near the market are excellent for a quick breakfast, and the sesame rings (koulouria) sold from carts near the port are the correct thing to eat while waiting for a ferry.
For sit-down coffee and something sweet, the neighbourhood around Agios Nikolaos church has a concentration of old-school kafeneions where a Greek coffee and a piece of galaktoboureko (custard pastry) will cost you very little and last as long as you like.
Photo: Tilemahos Efthimiadis / Wikimedia Commons (CC BY-SA 2.0)