I'd caution against trying to see San Gimagnano with a day tour group. I did a tour that was supposed to go to SG, Siena and Pisa with a nice lunch at a winery along the way. At the last minute, they changed the itinerary saying nothing would change other than the order in which we saw the places, however, the leader was actually cross with people for wanting to take a few minutes to buy wine after the lunch (which I suppose is the whole goal of doing the lunch for the winery) because we were late for Siena, then by the time we got to SG, it was already nearly dark and they said we had 1/2 an hour to wander around before we had to meet to get back on the bus. It was terribly disappointing, but what could I do at that point? My experience may have been rare, but it reinforced my feelings of dislike for tours, even just for a day. If you go on your own, I think you have to take a train from Florence to a nearby town, then switch to a bus to get there.
I agree with the others that Siena is well worth a day trip. I'm going back to explore more at some point because I'm sure I missed a lot and I like wandering with no time frame when possible. If I recall from reading here previously, a bus is the best way to get to Siena from Florence.
Bologna is also a nice day trip from Florence, although it's been hit by flooding recently. Pisa was a hard no for me. The tower is interesting, but even in mid December, which is not a high tourist season like the summer, there were sooo many people everywhere doing the typical pose to look like they're holding up the building so it felt more like an amusement or a curiosity rather than a historical site. The good news is that even on my worst day in Italy, I'm still in Italy, so that makes it a pretty good day.
Oh, Fiesole is a super cute town with amazing views down over Florence. It's about 1/2 an hour away and an easy bus ride (sit on the right side leaving Florence if you can). I really enjoyed wandering around the ancient amphitheater and just the town in general.