I wouldn't suggest you to drive in the city center and parking in Florence gives really hard times and it's really expensive. The easyest way (and also the most expensive) is leaving the car at the parking under the railway station and than everything is withing 10-20 minutes walking. Otherwise you can leave the car in the parkings just outside the center and then catch a bus. There is one in Piazza Vittorio Veneto (in front of the Cascine park) which costs about 2€ per hour, in front you find the bus stop, with N°1 you are by the Duomo in 10 min.
Thanks smilla ~> appreciate the help :>)
I have used many times the one at Porto Romano near the Pitti Palace. It's a good one if you come off the autostrada at Certosa exit(Chianti). Just follow towards the center and Porto Romano. Go around the Piazza and stay in the right lane the parking is on the right and there are always alot of spaces. The Ponte Vecchio is only a few minutes away. After sightseeing, you can drive up to Piazza Michangelo which is a close drive(n center traffic) after exiting the Romano parking.
The parking is free at Michangelo, but for only a short visit.
Thanks Rick, it's always good to hear of services that others have used and are pleased with. Much appreciated!