Best stops between Rome and Florence?

We're taking a big family trip next month and have hired vans scheduled to take us from Rome to Florence. Because we have flexibility by driving, we want to make some stops along the way to break up the trip and see some other cities along the way. My father-in-law had originally suggested a tour-group-style schedule that had us stopping in Orvieto and Assisi on the way up to Florence and then taking a day trip the next day to Montalcino, Siena, and San Gimignano. We don't want to lose the day in Florence, though, so we're trying to consolidate the extra cities into the travel day.

So, what is a reasonable set of cities we could see in a day? It seems that going to Orvieto, Siena, then San Gimignano can make sense to split the drive, but if we only have a few hours in each, will we be too rushed to appreciate these towns? I want to show my kids some of the variety of towns in Italy, but I don't want us to constantly be rushing back to the vans to get to the next stop. Any suggestions are appreciated.