Ring Café: The key here is to get a seat outside. Then you can begin your day with eggs done the way of your choice accompanied with orange juice, toast or whatever else takes your fancy. Again, prices aren't extortionate given its location so don't be wary of sitting down.
Pizza EATaliano: If you want to people watch while munching on your pizza, this is the perfect option. Part of a chain (don't fret though), this restaurant serves a mix of pasta dishes and pizzas with prices that don't match its location.
Osbudavar Pizzeria: This pizzeria is just seconds from the Fisherman’s Bastion and St Mathias Church. Staff are friendly, the selection of pizzas is good, ingredients are fresh, and, considering it’s touristy location, it’s good value also.
Great Market Hall, IX Fõvam tér: You'll find a large selection of fast-food type restaurants upstairs here. Expect anything from traditional Hungarian sausage, some similarly traditional goulash, or maybe just a plain ol'slice of pizza.