If you want to live the experience of staying at a 700 year old place, next door to the Pitti palace and Ponte Vecchio, this is the place. It is not on the tourist side of the river, but on the residential side. However, if you are driving, be aware that this is a car restricted area so non-residents get an 80 euro fine if they drive in. And they use cameras to get you.
The place has several “quirks “, but we managed.