James - with a car my advice would be to stay somewhere outside of Florence. We have been in Tuscany twice now, both times with a car and really enjoyed driving around. Our first trip we stayed for a week in an agriturismo that was about 1/2 hour from Florence. We drove to Florence one day and parked in the lots outside the city, no problem. Another day we drove to the local train station and took the train into Florence for another 1/2 day visit. This was during the summer so Florence was very crowded and people tell me I didn't really get to see it at it's nicest. But for us, at the time, 2 short day trips into the city were enough for us and we were glad to be staying outside. We spent the other 5 days driving around, went to Siena, Assisi, small towns, wineries, etc.
Our second trip we stayed in Pienza, or really, outside the city at a little B&B. From there we did day trips to Pienza, Montepulciano, & San Quirico. We also stayed 2 nights in Lucca, seeing San Giminano on the way. We really enjoyed Lucca and it was a very short trip to Pisa.
Bottom line - when you look at a map of "Tuscany", it is quite a large area. If you have 2 full weeks in the area, you could pick 2-4 different towns to stay in (including Florence if you like, though make it at the beginning or end so you don't need your car). Use those towns as your base and drive around to see the different things. If you really are open, then don't miss the Val d'orcia area which is where Pienza, Montalcina, Montepulciano are. We thought that was a very special, very beautiful area. I highly recommend the B&B we stayed at, which was Le Traverse, but I'm sure there are many other wonderful little places all over the Tuscany region. You will have a great trip no matter where you stay.