An extraordinary experience! I was staying in a large attic room with kitchen facilities, more of an apartment, with an entrancing view of the Duomo. Every day, as I left or entered, I was passing though a museum, which is what this 600 year old Palazzo really is. You are at the north end of the old city, every street of which feels like a history lesson. You are almost around the corner from the Accadamia and David, as well as several other museums and churches., but a bit of a walk {20 min] from the Uffizi and the river. There are stairs involved. The elevator take you up two flights, but you have to walk the last flight. You have a private bathroom with excellent water pressure, as hot as you want it, with a washing machine[!!]but its about 6 steps down from your room. So a few small negatives, but the positives FAR outweigh them.
If you can, get Roberto [he's actually a Duke, but never mentions it] to take you on a tour of the house and grounds, and he'll tell you of the 800+ year history of his family in Fienze