Florence to Siena by Car

I would suggest the Chiantigiana. See also this link This famed route will take you through the heart of Chianti.

It will take you ~45 minutes to reach Greve, which would make a nice first stop. Castellina, Radda and Gaiole are good stops. Check for wineries in the region where you could stop at lunch or shortly thereafter. I'd recommend Castillo di Verrazzano, but you'll be too far down the road by lunch.

San Gimignano is not on the Chiantigiana and maybe a stretch to reach. There's plenty to see without it and I'd go for a more relaxed ramble than to try to squeeze in too much.

You can drive the beautiful and historic Chiantigiana route 222 between Florence and Siena.
Charming towns to visit are Greve, Panzano( upper and lower towns), and Castellina. Take a short detour off of 222 to visit Radda to the east and another detour to visit Monteriggionito the west. Visit San Gimignano another day as it is fsther to the west and combines well with Volterra.. You realize that itSan Gimignano will be packed, lots of tour buses so your timing for a visit is important. Find out what time the buses come and go before leaving Florence. Call their tourism office.

Great suggestions. Appreciate your help. I think we will skip San Gimignano in order to have a more leisure/productive day.

I would take the Via Chiantigiana SR222 from Firenze Sud and drive it to Castellina. It’s a 1.5 hours drive at slow speed (add pit stops to that).
But then from Castellina I’d take the Strada di Castagnoli down to Poggibonsi (30 min) and from Poggibonsi I would visit San Gimignano (Poggibonsi to San Gimignano is less than 30 min drive). Spend a few hours there and you can check SG off your list.
After that you can head to Siena. Monteriggioni is along the way and there is a freeway exit that makes it easy for another quick stop. However I don’t know how much time you will have left at that point. But don’t despair. Monteriggioni is so close to Siena that you can easily go back there from your Siena base.

definitely SR222 ...beautiful drive

I would particularly recommend Panzano on this trip. I assume you have a hotel in Siena with parking but if not both Palazzo Ravizza and he Athena are hotels within the walls that have parking. At the Athena you need to book ahead as it is limited.

Thanks all. Good ideas. Should be a nice day.