Tuscany- Timing Suggestions To Explore

After a week on France, we will be in Tuscany late September Tuesday afternoon - Sunday morning before traveling to Cinque Terre for 3 nights. We are only using train and bus. We have 3 nights reserved in Siena Tues- Friday. We plan on exploring from Siena but we don’t want to be too rushed. We will enjoy the town, go on a bus tour to explore other towns for a day, find a cooking class, and possibly hire a driver or go with a smaller group to visit a winery or 2 without a giant bus tour if that is possible. Open to other ideas. My question is - do I book another night in Siena to get more out of the area without checking out and checking into another location( 4 nights total)? Or do we stay 3 nights in Siena followed by one night (Fri- Sat) in San Gimignano to experience that town after the tourists leave? Then do we take a bus to spend one night in Florence to be close to public transportion on Saturday to leave for CT on Sunday? Or after 3 nights in Siena do we spend 2 nights in Florence? If we do spend a night in San Gimigano, I didn’t want to be stuck there on a Sunday due to possible transportation issues to get to CT and that is why I thought of leaving there by Saturday. I need help where to book in Tuscany to make the most of our 5 days or so. I do want to see a few places on Florence, and experience a large town for a bit, but not everything - not our main focus. Thank you for your expertise and help. I have never been to Europe and trying to make the most while trying to take it in to enjoy.