Driving inside the historic center of Florence is virtually impossible. Only residents with permits are allowed to drive there.
Enforcement of the "Limited Traffic Zone" or "ZTL" is by camera. Violators will be tracked down and fined, but the fine may not arrive for a year or more after the infraction. The fines start at about €90. Once you enter the forbidden zone, it is virtually impossible to pass only one camera, and each time you do, it is a separate fine.
In addition, Florence has some of the tiniest streets in Europe, an amazingly fiendish one-way system that confuses even the locals, and some streets that just come to an abrupt end, with little or no warning.
Parking on the street in the historic center is out of the question. It may only be done by residents with a permit, and all other cars are towed away instantly - if not sooner - to some godforsaken suburb from which it will cost you hundreds of euros to get yours returned.
That said, you may be able to arrange a very temporary - about 30-minute - exemption through your hotel, which will need your license number and other information to make arrangements with the authorities. You will then have to get the car from the hotel out of the ZTL before the exemption expires.
A car can be useful to reach some destinations just outside the city centre, like Fiesole or Settignano (these sights are also reachable by bus service), or for day trips to wonderful places such as Siena, Volterra, Arezzo, etc. It is possible, if a bit tricky to rent a car in Florence and get out of town and back to the car rental agency without violating the ZTL. Those tempted to do so, should make sure to get precise directions from the rental agency.