I would highly recommend Patrizia's place. It's clean, spacious and located right where you want to be to walk to all the historic sights. Lots of food options nearby and the garage parking is a rare perk. It isn't set up for children per se, and we didn't expect it to be, but once we moved some art out of reach it worked great for our two young sons.
We will be staying with Patrizia again when we return to Florence.