Tim,
Two years ago we spent a wonderful week in Tuscany. We stayed just outside Greve, which is south of Florence, at Castillo di Verrazzano. The winery has agriturismo accommodations. The rooms are comfortable, very reasonable and kept neat as a pin. The agriturismo is near the road leading into Greve, about 3/4 mile from the winery itself. Be sure to book with the breakfast, which is scrumptious. It includes wild boar salami and other cold cut, several cheese choices and wonderful bread, along with standard breakfast items such as eggs and cereal.
Also plan to take the tour of the winery. I highly recommend the Wine and Food Experience. They aren't kidding, plan to spend at least three hours! Also eat a light breakfast and don't plan on needing to eat dinner! When we were there, the owner and the wine makers were sampling the newest vintage and the owner kept bringing over extra samples to try. Luckily we were staying on the property because we weren't in any shape to drive on the highway!
If you want to take cooking classes, Greve is just 5 minutes away. La Cantina offers cooking classes led by Mamma Lorena, the mother of Alessandro, the owner. We didn't take cooking classes, but can attest to the wonderful food they prepare. We ate there the first night we arrived in Italy and Alessandro and his staff went out of their way to make us feel at home. Since it was off season, we were the only tourists there that night. It is a favorite restaurant of the locals, which I consider to be a great testimony.
Greve is a great location to use as a home base. It is on the famed Chiantigiana (SR222) road from Florence to Siena. We visited the places described in the link. We also spent a day touring San Gimignano and Volterra, which are an easy drive from Greve.
Driving in Chianti is easy. Just be aware that there are automated speed limit checks both in the countryside and in the towns. ZTL's are clearly marked and easily avoided. Greve does not have a ZTL, but we found it easier to use the large free public parking lot and walk over to the piazza.
I understand that many are restricted to going on vacation from June to August, but I would suggest you try to visit a little earlier, such as early May. It won't be as hot and crowded then.
Finally, I highly recommend taking Walks of Italy tours in Florence. We took the Best of Florence walking tour and the Uffizi tour. They were well worth the cost. Our guide Marco has a graduate degree in history and did a wonderful job of describing what we were seeing. They keep the group size small and the cost includes skip the line tickets.