The two of us will be in Tuscan in late September. We will do 4 days in Florence and are planning 7 days to see Tuscany. We will have a car. Do you suggest staying at different locations or staying at one central place?
Whether you should stay in a central base or move around while you're touring Tuscany depends a lot on the places you plan to visit on those 7 days.
If this is the first time you come to Tuscany, then the majority of the main "attractions" in Tuscany are concentrated in the area between Florence and Siena (Chianti), to the west of Siena (San Gimignano, Volterra, Monteriggioni) and to the south of Siena (Montalcino, Pienza, Montepulciano). Of course you should also see Siena itself .
I think staying somewhere around Siena (not in the city itself as then you'd have to worry about parking fees and area restrictions) or to the west of Siena would be the best solution and thus you might be able to stay in that one central place the entire time. Most day trips in the area would all fall within an hour's drive from that area. You could stay at a country estate at farmhouse apartments such as at Cabbiavoli, for example.
If you want to reduce driving time to a minimum, you could divide the 7 days into two and stay to the south of Siena for one part and then closer to San Gimignano/Chianti area for the other.
Pisa and Lucca would be about a 2 hour drive each way from Siena, if you want to visit those then I would definitely suggest breaking your week into two and for the second part looking for places in near San Gimignano or in Chianti (see Casolare di Libbiano or La Roccaia for example).
Let me know if you have any further questions, I'll try my best to help out.