parking near florence

We found an underground parking lot about one mile due north of the Duomo - and managed to get in and out without getting a limited traffic zone ticket. We still had to deal with traffic and a map that wasn't suitable for the city (didn't have a GPS). If I did it over, I'd go with your idea and find a local train that could get me into town with less traffic and less worry about a ticket.

For Venice: There is a high rise car park in Mestre directly across the street from the Venezia-Mestre train station that I have used happily for several years. For Florence:
I used to park under the station in Florence but now would prefer not to as the dreaded ZTLs have propagated and I don't want to go the wrong way. Also Florence traffic has to be seen to be believed. The nearest station outside the area so thoroughly covered by the dreaded ZTLs is Prato.

I used the same car park in Venice, rather than the large parking lot most people use. I liked that it was secure, the car wasn't broken into during our stay in Venice. I didn't like that it was expensive and that it took about an hour and a half both getting parked and picking up our car, which really cut into both travel days. For Venice, I'd park on the mainland and take a train in.