In Florence the lady and I always stayed at the Soggiorno Battistero B&B (link below) in Piazza San Giovanni. You can't beat the location and the American woman (Kelly) and her Italian husband that run it are great. It's very straightforward, nothing extravagent, but very clean and great service. Ask for breakfast in the morning and they'll bring in some juice, coffee, croissant, etc. I'd also ask for a room that's window opens up onto the Piazza with a great view of the Baptistry and the Duomo. If you're there on a Friday or Saturday night expect a little bit of noise but, then a again, is there anywhere in Italy you can stay (any time of the week for that matter) in which you don't here noise from the locals at all times of the night??

http://www.soggiornobattistero.it/