I spent 4 days in Florence and stayed with a friend who lives just north of Centrale Mercado. I was able to use one of his bikes the entire time. It was a short 10 minute ride into the center and was a fantastic way to get around. Not to mention, on wheels you can cover a lot of ground!
I would highly recommend renting bikes during your visit. Florence is a bike friendly city -most people commute on bicycles or mopeds. there are plenty of places to lock and park.
There are many cyclists in Firenze - none of them wearing helmets. The cars and scooters seemed to drive quite peaceably. No honking, no madness - not even on the road which circles the duomo. Of course - this was November.
But many of the streets have very narrow pavements. If someone is walking towards you one of you has to step onto the road. As there were few people about this wasn't a problem. But I can imagine it would drive you into a frenzy in the height of the tourist influx. I was trying to imagine how you could make each pavement one way - that would help - but that is probably never going to happen.
Sunday evening is the time of the passegiata. All the babies are taken out for an airing. The Disney shop had a queue banking up down the road. Then by 8 everyone had gone home. Of course it was rather cold. Maybe it is longer when the weather is warmer. It is very pleasant to stroll around with the locals, trying to mingle and blend in.
I think the best way to visit the Florence City Center is by bycicle. You can enjoy the landscape, palaces, architectures, arts, people with your bycicle. There are many bycicle streets along the river, in the avenues. Moreover the city center is forbidden to cars so if your hotel is not inside the city center you can go there renting a bycicle and enjoy your stay. If you park your bycicle somewhere lock it!!!!