I am planning to take my wife and two teenagers to Tuscany (San Gimignano, Siena, and Volterra - among other places). I have a car and will be there 3 nights. Should I stay in a city (e.g., Siena) or rent a country house that is central to most towns and make day trips?

What time of year?

Where will you be coming from and where are you headed after Tuscany?

What are the "other places" you want to explore?

Generally speaking, we no longer enjoy staying IN Siena if the plan is to take several driving trips to other towns. There's just too much traffic now for our tastes. But we also don't enjoy staying so far out of a town that we can't walk in for dinner.

Look at Fattoria Tregole and Casanova Pescille.

Or, if you want a nice hotel in Siena with easy driving in and out, look at Hotel Santa Caterina.

Jean,

I will be there in August. I am coming from Cinque Terre
, Pisa, Lucca and then off to Florence.

Coming from Pisa, you could travel to the Volterra/San G area on your way to your base in Tuscany (or a slight detour on your way back to Florence). I would pick somewhere south east of Siena towards Pienza, but it would be a trek to Volterra/San G. You could also stay somewhere like this more in the Chianti area not far outside Siena.

http://www.mulinodiquercegrossa.it/

Countryside is fine and perhaps even better if you plan to visit Tuscany because distances are very short and in less than 1 hour you can reach Florence and Siena if you stay in Chianti.
Here you can choose to stay among the vineyards or in a small village as San Gimignano (Volterra is a beautiful but a bit more faraway).
As for Chianti I can suggest you to stay at Borgo di Pietrafitta (http://www.borgopietrafitta.com).
As for San Gimignano Casolare Terre Rosse (http://www.hotelterrerosse.com)