Tuscan Public Transportation Hub

Florence is the transportation hub for Tuscany. If you plan to make many train visits, that is really the only good place to stay. With bus transport you might find other options.

What do you mean by large group? Do you have enough people to hire a large van or small bus? It would be nice to have a tour guide with you to enlighten you on what you are seeing.

You might find the Rome2Rio website helpful for high-level scoping-out of transportation options. Understand that you can't trust the fares it displays or (sometimes) the travel times. But it's pretty good about showing when a train is available, when you'll need to take a bus, and when you'll need to take two buses to reach your destination. Those two-bus trips can be really slow and annoying. Train + bus combos are sometimes even more fun.

One thing to keep in mind is that, sort of by definition, the train station serving a hill town is not terribly close to the historic area you want to see. It will be an uphill walk. So for many destinations in Tuscany, if you travel by train, you'll need to add a taxi ride or local bus trip up to the top of the hill on which the town is perched. It's part of the charm, but it certainly doesn't speed things up. This is one reason folks take a lot of bus tours and van tours in Tuscany.

Those local day-trips (some of the specialized ones being quite good) nearly always depart from a major city. I guess you might find some options from Siena (Googling will find them if they exist), but most will probably require that you get yourself to the pick-up point in Florence quite early in the morning. That would be a drag. If a van-full of your groups agrees on a particular itinerary, you might be able to hire a private driver to pick you up at your lodgings and head out from there. But if one or just a few folks decide to take a packaged day-trip to Lucca or Volterra/San Gimignano, there is likely to be a very early wake-up call required.

Is there a reason you don't want to stay in Florence? That's about the most convenient transportation hub for Tuscany.

Florence is best. But it also depends on what you want to visit. Siena is also good for some localities.

Thanks so much for all of the prompt advice. We want to rent a villa, there are six women traveling, and a few of us have been to Florence more than once. So we are not looking for a City experience. We don't mind walking, and hope to avoid the expense of a driver which I understand can be several hundred dollars a day. Sounds like renting cars might be the way to go. But again thank you so much for all the great advice

Rent a villa in the Siena area, or somewhere between Florence and Siena.
For your plans you need 2 small economy or compact rental cars. Two economy cars are cheaper than one minivan. Actually you can rent 3 economy cars for the prize of a minivan.
Having two vehicles also adds flexibility in case some of the girls in your party want to go out on their own to look for some hunky Italian men to hang out with.

If you're planning to rent cars, you may find this helpful.....

It's important to note that for driving in Italy, each driver listed on the rental form must have the compulsory International Driver's Permit, which is used in conjunction with your home D.L. These are valid for one year, and easily obtained at any CAA/AAA office (two Passport-sized photos required, which may be provided by the issuing office). Failure to produce an IDP if requested can result in fines on the spot! Failure to pay the fines when requested may result in the rental car being impounded, and further charges for towing and storage. Have a look at https://it.usembassy.gov/u-s-citizen-services/local-resources-of-u-s-citizens/transportation-driving/ for more information on I.D.P's and driving in Italy.

You may also want to have a look at some of the other posts here concerning the dreaded Zona Traffico Limitato (limited traffic) areas that are becoming increasingly prevalent in many Italian towns & cities especially Florence, which is almost saturated with automated ZTL cameras. EACH PASS through one of the automated Cameras will result in a €100+ ticket, which you won't know about until several months after you return home! This website provides more information - http://www.slowtrav.com/italy/driving/traffic_cameras_speeding.htm

There's also the issue of parking tickets, high fuel costs, tolls and automated speed cameras including the devious Traffic Tutor system which measures not only instantaneous speed but also average between two points. Violate either or both parameter and expensive tickets will follow.