Mixed experience.

PROS
Apartment located in a really authentic old house that is amazing. Location is great as well: the heart of Florence and couple of minutes from main squares of the city.

CONS
The room does not feel very comfortable: climate system does not do its job well: it was either cold or stuffy; the room lacks some tiny necessities like teapot and hair-drier (though it is fair to note that hair-drier was provided by request).
Stairs to the above level are not nice: they are made of steel and cold because of that. Hot water is supplied by water boiler so it can finish when you are in the shower (happened to me twice).
Another disappointment was that the owner demanded 20 euros for late check-in (1 am). He was quite persistent about it though this rule was not on the contract.

Summary
Should be a good option for young people not freakish about comfort but be careful with time of your check-in (see above why).