Well, you seem to have asked the tuffnut question of the week.
Here is couple of places I have enjoyed. I have others but further away in Umbria, Le Marche and Abruzzi.
Just outside San Gimignano, Villa Bacioli. https://www.villabaciolo.com/en I dealt directly with the owners via e-mail. Four of us stayed there back in 2010. Other guests were there also. I am sure each room has its own on suite. We did. Also, a couple of apartments are offered. Had breakfast every morning on a delightful patio looking northeast to San Gimignano, nestling on the hill a couple of kilometres away. Dinner was available with adequate lead time notice. Tried it one night and it was excellent.
We stayed from 26th Sept until morning 1st Oct. Visited Pisa, Siena, Florence, Volterra and Grieve and Chianti on separate days. The driving and parking were easy for us. Spent about an hour each day in San Gimignano just because it was close by. The pool in the early morning. Temps were in the 18c to 21c range, cool but no rain. Harvesting was underway, stopped to watch and scored a chat with a team that was having a morning break. Heard about Villa Bacioli from a mate who was told about it by a mining exec he met in Brazil. Multicultural appeal. It was ideal for us. Good reviews of late.
2018, 8 years later to the east in Cavriglia took Villa Poggetta for a week, 22nd to 29th Sept. My girls tell me that they dealt directly via the villa’s website and by telephone. Does not show up with a website at present.
Booking appears to be through Posarelli Villas as Villa Poggetta (https://www.posarellivillas.com/italy/tuscany/cavriglia/2269) or
Booking.com as La Villa di Promo. Try variations in your browser and see what happens.
A spacious, well-appointed villa in the Tuscan style. You will see that from the pictures on the web. Had dinner at the villa on the first night. No one can remember if it was part of the deal or if we asked for it. Probably because we consumed too much of the farm’s wine and enjoyed the food. The villa was perfect for us 8 adults and 5.20 children. Rest of time did our own cooking. Tomatoes and other vegetables from the garden, or roadside stalls or local co-op.
Over the week we drove to the following for a day each. Stopped in the countryside for picnics and generally relaxed soaking in the ambiance. Montepulciano, Florence, Grieve/Radda in Chianti, Siena (stayed until about 10pm into the evening) and Scarperia, which is north east of Florence. The temperatures were between 24c and 28c. The pool was used frequently. Particularly refreshing in the late evening. Grape and olive harvesting in full swing.
My daughter-in-law and I can speak enough Italian to get by, and make bookings over the phone with wine cellars that appeal to us as we drive around. We leave somethings for on-the-spot choices. I suspect where ever you select to stay, the operators will be able to arrange chef/vineyard appointments to your liking. Hopefully someone with experiences will provide more information on your questions. I can give you some hints about parking in Siena.