Florence, staying outside of

Not knowing the rest of your itinerary, I can only make a 'stab in the dark' suggestion.

Plan your trip so that you can pick up the car as you leave Florence and go to the places you need the car for OR have Florence be the end of you car usage and drop it off as you arrive.

If neither of those is possible, then a bit more info about your itinerary would allow folks to make useful suggestions that fit your parameters.

We arrived in Florence by train, stayed in the city and then walked to the car rental place to pick up our rental car at the end of our stay there. I highly recommend that you do that if at all possible . It was very stressful just trying to depart the city after we picked up the rental car so do what you can to avoid having a car there. What does the rest of your itinerary look like?

One option is to park your car in one of the outlying lots and stay in Florence. I believe Rick's guidebooks have information about those parking lots and transit from them into town.

If you prefer a smaller untouristy town, consider Pontassieve which is home to the Ruffino Winery. I went there for the annual food festival and was pleasantly surprised by how nice it was. The longish main street had lots of nice shops and restaurants. I didn't look for hotels, but Google maps shows there are 3 hotels in town and an "AgriResort" just outside of town. Trains to SMN take 25 minutes (20 to Campo di Marte), and they run frequently and late (although only about hourly late).

On one bus line are Barberino and San Casciano, the former is a bit further but nice in itself.
Another route includes Strada (not so pretty but closer to Florence), Greve and Panzano. I liked Greve, has a good market day (Friday or Saturday).
All within 30 - 55 minutes by bus. It's not a bad idea, will allow you to springboard into the Chianti area with your car.

Fiesole!
We’ve stayed there twice at Hotel Aurora (Room 11 has a huge terrace with an incredible view of the entire city of Florence). Parked the car on the street in front of the hotel for 5 days and took the 20 minute ride on the #7 bus down to the Duomo and back every day. Sweet!

Yes. Fiesole! We stayed at Villa Bonnelli and loved it. We did have a car but I can't remember the parking arrangements. The No. 7 bus is ideal for getting into Florence and is a picturesque drive, as well.

We stayed in an agriturismo just outside Greve and took the bus into Florence it worked great! Our focus was exploring Chianti. If your focus is Florence, staying closer in might work better.