My wife and I stayed here for 5 nights with our 15 month old daughter. A high chair and cot was provided which is good.
Check in was fairly smooth and was completed by Stefano's friend Thomas, who showed us around the apartment and told us what attractions, restaurants and shops could be found nearby.
You really are in the heart of Florence here and can literally see the church's dome from the kitchen window. Pretty much everything you'd want to visit is within walking distance. We found this useful as you could come back half way through the day for a break and then go back out.
The space itself is quite large and has everything I expected, as described in the listing. It is on the 4th floor but is serviced by a small lift. You can also hear the buskers performing at the end of the street below at nights which I thought was nice.
The host was also responsive to any questions I had, even ones that were about where to find the best leather goods.
All in all I'd recommend staying here.