Florence ...
These are our favourites. Again, traditional fare -- that is after all what Italians do best. I can give you addresses and times for these and the Rome places, but they're likely also on the Net.
Coco Lezzone. A classic. Inexpensive, well-executed Tuscan fare.
Vini e Vecchi Sapori. Close to the Palazzo Vecchio. I could easily eat here every day (as some locals do). Only five tables, so be early or be patient. Mom's in the kitchen, Dad's at the salad and cheese counter, son is the server. Simple, straightforward Tuscan fare, but somehow eye-opening.
In Fiesole, in the hills above Florence, there's I Polpi, which we've only been to once but really liked. A little more modern in approach to food, but still well done and not too far from the traditional.