Parking in (or near) Florence

Forget the bus.
If you come through the freeway (Raccordo Firenze-Siena) the easiest is to go to:
PIAZZALE DI PORTA ROMANA (use Google maps to see directions).
Right there you can find the Piazza della Calza Parking (just behind the city gates). It's €2/hr (€20/for 24h).
You could also go up to PIAZZALE MICHELANGELO (use google maps again). The parking there used to be free, now it's no longer free, but just a short distance from it, you can still park for free (I think) near the San Miniato church. From there, after you see the view, you can go down to the city center on foot (20-25 min walk). Coming back up is uphill however, therefore if you are not up to it, you can take a taxi.
If you decide to drive the via Chiantigiana (Chianti Road) SR222, then you'll probably end up on the via Marco Polo. Just turn left when you cross the bridge (stop light) and drive straight as long as you can. Eventually you'll have to turn right on viale Amendola. After 200 mts. there is plenty of pay parking on Piazza Beccaria. Also nearby there is the underground parking of Piazza Sant'Ambrogio. Also on Lungarno della Zecca Vecchia there is plenty of pay parking.
The important thing is to know the colors of the stripes on the ground:
BLUE: Pay parking (meter should be nearby, just buy ticket and place on dashboard)
WHITE: In some places it means free parking, but in Florence it's generally for residents only, although none of my friends and relatives give a damn about that and park there regardless whether they live in that area or not (I'm not encouraging you to break the law, but Florentines will park on your feet if there is enough room for the car and they can park for free)
YELLOW: Restricted parking (handicapped, official vehicles). You shouldn't park there, although my father always parked in the spots reserved for police cars when he was alive, because he said that nobody would ticket a car for fear that it belonged to a police officer. He always did so also at the Florence airport. Apparently he must have been right because he was never ticketed or towed away. My wife used to laugh her head off each time my father did that, I'm pretty sure he's now parking in heaven in the spot reserved to St. Peter.

You can park at the Michaelanglo overlook for free. ( in 2013 but Roberto posted sayin that has changed )
When I was there last August, it filled up early in the day and was a bit of a zoo with vendors and crowds but a great place for sunset. You can take a bus to downtown from there.
Enjoy the trip!

Thanks very much to both of you for your great suggestions! Excellent information on the parking colors, too. Roberto, your father's perspective sounds a lot like my husband's...we'll try to stay out of trouble, though. ;)