We've spent about 10 days in Florence over two trips in the last six years, and truth be told a fair amount of the meals were forgettable or too tourist-hyped & expensive. Here are three places, however, that we've really enjoyed and have returned to multiple times:
Ciro & Sons on via Giglio--
http://www.ciroandsons.com/. Wonderful, family-owned, reasonably-priced, more southern Italian than Florentine, which I prefer anyway. Standouts are the Margherita pizza, the antipasto della casa (grilled vegetables), and the calamarata all' amalfitana (squid over flat noodles, incredible, squid ink-based sauce).
Ristorante Toto on Borgo santi Apostoli--
http://www.ristorantetoto.it/en/. Traditional bisteca alla Florentine, but a nice twist instead of a big slab o'beef is that this is sliced like a London broil, on a bed of arugula and rocket greens dressed simply with phenomenal balsamic vinegar and olive oil. Near the Ponte Vecchio.
Da Nerbone at Mercato Centrale--
http://www.walkaboutflorence.com/what-to-do/da-nerbone. The Firenze version of the Italian beef. For 3-4 Euro, boiled beef on a round fresh roll with no
au jus but a pesto sauce. I wanted to eat one of these almost every day for lunch if I was in the vicinity.