Most of the dining spots listed below are relatively inexpensive and serve authentic, Tuscan food.
Trattoria ZaZa: Located near the Mercato Centrale, it is full of fresh Tuscan dishes like pastas, meats, but not much in terms of fish. The appetizers are delicious with chesses and sausages. Sit outside on a warm night or anywhere inside is good too. Good service, inexpensive. http://www.trattoriazaza.it/
Il Bordino: Friendly service located just over the Arno in Oltrarno. Rustic dining and friendly service. The desserts are the best but don't miss the Bistecca Florentino for just 10 euros at lunchtime. The risotta is good as well as the meat dishes. http://www.trattoriabordino.it/home.html
Trattoria Trebbio: We usually save Trebbio for our last meal in Florence because it is so good. A busy little place is the spot for Bistecca Florentina and other local dishes. I don't recommend the tripe. Located at Via delle Belle Donne, 47, Florence, it is a bright and cheery place.
Ristorante Osteria Zio Gigi: Concentrate on the appetizers here. Good cheeses and meats. The pastas are so-so. However, you will have a lot of fun here when "the fat guy sings". Very inexpensive and a good time out.
Il Latini: Wow! Do they serve a lot of food here, family style. Just when you think it is all over, they come out with more. Perfect for a large group.