I agree with Kent. A car in Florence (and in Rome) is not worth the hassle.
I'd give myself a day to get over the jetlag. Go for a nice walk along the river, see the Ponte Vecchio, etc. Then take another two days to explore Florence. The city is pretty compact so I don't know that there's a particular best area to stay in. We stayed in a hotel near the Ponte Vecchio which was well-located although I didn't think the hotel was worth the money. As long as it's centrally located or near one of the big sights, you'll probably be happy with it.
I'm slightly unsure about the length of your trip. Do you mean that you have about 10 days in total? Generally one-night stops are not popular on this board as they're tiring, a hassle, cost more, and prevent you from actually enjoying the places you're trying to enjoy. You also can't generally count the day of arrival/departure as jetlag and flight issues make those days unreliable at best.