We just returned from Florence and wanted to pass along two recommendations.
For hotel, we stayed at the Hotel Dali (www.hoteldali.com). This is a great, reasonable and very friendly place that is located three blocks away from the Duomo. Marco, the owner, is extremely helpful. If you're a light sleeper, request a room away from the street. Rates for a double with bath are 75 Euro.
I'd also like to reccomed Il Barroccio, a very authentic, friendly restaurant right near the Bargello (Via della Vigna Vechia 31r). Get the assiago primi (the mixed pasta and soup sampler) and the bistecca for two, which at 33 Euro is the most reasonably priced in Florence. The food is absolutely great and the owners are very welcoming. We ate here three time in two weeks!