Il Latini

This is the place to go if you want to try real food from Tuscany, including traditional soups and the famous T-bone steak.
The food is really good and the price is fair. You can order everything from starter to dessert and pay around 30 euros (of course it's the steak that makes it expensive).
This restaurant is located in the historical center so you can easily reach it during your sightseeing trip.
I think opening hours are noon till 3 p.m. for lunch and 7 p.m. till I don't know when for dinner.
Since it's always very crowded, I recommend going there a little while before it opens. You can just wait outside and as soon as they open, they'll let you in. There's plenty of room, but if you arrive later, it's unlikely that anyone will give up their seats soon.
Reservations are pretty useless too in my experience, because if you call they'll just tell you to come at opening time!

This is in my top three dining experiences of all times. I went here with my mother whenever we did a tour of Italy. I had studied in Florence but had never heard of this place. I read about it on Chowhound and decided to try it out. I am SO glad we did. The rustic Italian food was so incredible. everything was prepared just right. The service was immaculate. Our server ended up giving us dessert and after dinner drinks for free. His suggestions hit the mark exactly. The place was crowded and hectic, but we were never forgotten about which is a feat in and of itself. Seating is group style, which was nice. We talked to a girl from China who was on some type of study abroad program. She was freaked out whenever she saw we left a 20 euro tip because she thought it was super expensive. We assured her that our server had just earned it and it wasn't the typical 10-15% Go eat here, you will not regret it!