We stayed at Canto degli Scali. It is a unique property in that they have the options of a B&B or apartments. It is a recently restored 14th century Palazzo run by two brothers: Marco and Alessio who are wonderful hosts. It is in the heart of Florence a five minute walk from the Ponte Vecchio and 10 minute walk to the Duomo. It is near enough to the big sights, but in a small neighborhood that you don't feel like you are in the middle of of all the tourists. If you stay in the B&B, they offer a breakfast token for a little cafe around the corner.
I would definitely stay again. The only gotcha is that there is no elevator, so you need to climb a few stairs: here is the link so that you can check out the rooms and prices--http://www.cantodegliscali.com/en/.
I also highly recommend Eating Europe's Sunset Food Tour. You get the visit everything from the wine windows of Florence to local restaurants, we loved the gnudi restaurant (Tuscan gnocchi). It is a great place to get to know some local restaurants and then come back to explore more on your own.
If you love pork, try the Antica Porchetteria Granieri 1916. It is a take away Porchetta sandwiches for about 8 Euros, you get a wonderful meal.
We also loved visiting the Central Market, both for shopping and for dining. Since we stayed in a B&B with a fridge and stove, we shopped at the market one morning and then cooked a wonderful dinner at our B&B.