Trains are great to commute between major cities, but driving in Tuscany (or anywhere in Italy) is a necessity if you plan to see the countryside and do any winery visits.
On our first trip to Italy lasted 3 weeks. We flew into Rome (where we spent 5 days and could have stayed longer), then took the train to Venice (4 days), then picked up our car near the Venice train station and drove to Florence (3 days) and to Tuscany where we stayed at a farm house near Castellina in Chianti for 8 days with day trips to Sienna, Montepulciano, Montalcino and other smaller towns.
After that, we drove to Civita di Bagnoregio - worth a day trip (google it) - and finally dropped the car near the Rome airport and spent the last night at a cheap hotel near the airport so that we could visit Ostia Antica. The Roman ruins at Ostia Antica are absolutely worth a visit.
Our most recent trip (also 3 weeks) we flew to Venice, after which we picked up our car and meandered west through Verona (staying at an azienda agricola north of Verona and did visits to Giuseppe Quintarelli and a few other producers), Lake Como, over to Turin, a full week in Piemonte, and then dropped the car in downtown Milan where we spent our final 2 days.
If you do drive into a large city, be aware that you may require a permit to drive into town. We didn't know this in Milan and the car rental place (downtown) didn't inform us. So a month later we received a sizeable fine in the mail, as well as an extra "processing" charge from the car rental company - because the car was registered to the car rental company, so the police had to deal with them to get our contact info. A big money grab scam on the part of both the police and the car rental company.