3 minutes from the Duomo down a quiet street, we discovered Forno de' Ghiotti by accident when looking for a different place to have lunch. We ended up going back there for lunch almost every day for the rest of our week in Florence.
Fantastic range of freshly baked pizza, calzoni, bread and various other delicious things (the panini looked great as well); the lovely old guy who runs it doesn't speak any English but it doesn't matter, you can just point at what you want if you don't speak any Italian. A slice of pizza is €1.50-€2 and it ranks among the best pizza I've ever had. Go there. Go there now.