Sleeping in Florence-3 choices...

Don't know any personally, since I generally stay with my relatives when I go to Florence, but based on location I would choose the B&B Dei Mori which is in the original Roman district of Florence, next to Dante's house. No traffic in that area.
Residenza de' Pucci is on a street where buses run, therefore I wouldn't choose it, too noisy if you happen to face the street.

Another option, also recommended by RS and which I know, is the hotel La Scaletta, across the river on the Oltrarno. Very nice and beautiful views from the roof top bar/restaurant.

http://www.hotellascaletta.it/

Depending on what you're going there for and your ability/desire to walk I would highly recommend the Villa Medici. It is about 1/2 mile out of town but the hotel is amazing.

We really liked Soggiorno Battistero, but it may not be for everyone. Most rooms look onto Piazza San Giovanni, which is of course very busy at most hours. The room windows are dual glazed-we were on the 3rd or 4th floor-and they have heavy interior wood shutters and drapes on top of that, pretty effective at cutting noise and darkening the room-you could certainly find a quieter place if that is important. We loved being right there with a straight on view of the Baptistery, and the young family that runs the place is helpful, the wife is an American ex-pat so language not an issue. Simple breakfast brought to your room each morning, or you can opt out though not sure if there is a price break.

Villa Medici out of town?
It's in the historical center, on via il Prato.
Anyhow. It's a great hotel, but not the cheapest facility in town. So it also depends on your budget.

We were on a Rick Steves tour and stayed at Hotel Loggiato Del Serviti. We had a view of the Duomo from our room. It is on the same block as Galleria Accademia where David is shown. Great location and there is a washateria a half block away.

We stayed at Hotel Duomo, another RS recommendation. The Duomo is literally in your face. Not the cheapest place, it the location was excellent.

Sorry Roberto,
I meant the Villa Medici is 1/2 mile from the duomo, uffizi and palazzo vecchio areas of Florence

We stayed at Dei Mori in 2011 and really enjoyed it. It was in a good area and close to things we wanted to see. I am not sure if the management is the same but they were very helpful with restaurant recommendations too. There was at least one flight of stairs to get inside if that would be an issue for you. I don't think there was an elevator.

Soggiorno Battistero was excellent when I staid there in 2015. Not the typical setup of a hotel. But its right across from the Duomo and right in the heart off the city I thought. I could walk pretty much anywhere and the staff was wonderful. If I went back to Florence I would stay there again.

We stayed at Soggiorno Battistero in 2012 (before the new elevator). As Dave said, it may not be for every one. I liked it and my husband not as much. Wonderful hosts, reasonable price back then, good location, tiny bathroom, and smaller breakfast brought to your room.

I'm not familiar with the 3 you listed, but I loved the Hotel Torre Guelfa near the Ponte Vecchio and Uffizi. Great location, lots of character, friendly and helpful staff, great breakfast, and loved having a drink while sitting in the tower, looking out over the city!