My girlfriend and I had a wonderful stay at Guido's apartment in Florence. Central Florence is a small area and easily walkable, yet even then, the apartment's location can't be beat, mere steps to the Ponte Vecchio, and short blocks to all the major sights. The unit is definitely dated (another reviewer noted that it could use a thorough cleaning), but the convenience makes up for it all. Plus, Guido was always available to help answer any questions (he lives right next door).
Note that there is no central air-- just a floor AC unit that you'll definitely need to keep the unit cool-- and that there is a washing machine for laundry, but no dryer, so we had to air dry clothing after running it through the centrifuge function a few times. Also, the elevator is super convenient but if it's out of service for any reason you're in for a generous series of stairs to get to the unit.
Lastly, it's walking distance to the train station, but it's about as far as anyone will want to walk, and if you've got rolling luggage, you're in for some rough sidewalks (not as rough as Roman streets and sidewalks, but still cobblestone). We walked from the train station on arrival, but took a taxi when departing.