Piergiorgio's place is almost perfect. We stayed there for a whole month and found it very livable. The kitchen has everything you need to cook, a nice table and chairs for eating, the couch is comfortable, the AC/Heat units worked well, and the beds are comfortable enough. Plenty of hot water and good water pressure. You can hear noise from the street in the living room but the bedrooms are very quiet. The washing machine works well and there is plenty of drying space with the 2 drying racks.
The location is great. We walked everywhere, no need for a taxi. A 5 min walk from the train station if you want to do a day trip. There are plenty of really excellent restaurants within 2 blocks, the Central Market (upscale food court on the top floor, food stalls on the bottom floor) is 1 block. There is a good size (for Florence) supermarket just 2 doors down which has pretty much everything we needed.
There isn't much storage space for your clothes and stuff. Just the 1 armoire in each of the 2 bedrooms - no closet, no shelves. This probably isn't an issue if you aren't staying for long.
There is one flight of steps leading up to the apartment. Only 10 steps but it's pretty narrow.