About a 3 minute walk from Piazza della Signoria in central florence is a hole in the wall eating establishment that just may be the best cheap restaurant in Italy, La Prosciutteria. You walk in, order at the counter(they can't serve you as it is technically not a restaurant) and set down with a glass of great reasonable priced local vino. Moments later a long piece of wood covered in local awesomeness arrives and the battle at your table begins and all conversation stops. Three hours later you stumble out, full and drunk, and try to figure out the maze that is Florence as you attempt to return to your hotel. Next night you swear you will try somewhere else but you end up back here, repeating yourself.
Make sure to try the Creamed gorgonzola with black truffles.