I'd spend a couple nights in Florence, and then pick up a car and go to a base in the countryside fo

We are planning a first trip to Italy for the last 2 weeks of October. We are planning 3 nights at the beginning of the trip in Rome and 3 nights near the end in Cinque Terre. We were thinking about spending the balance in Tuscany and would appreciate suggestions on places to go or stay. We are considering 2 to 3 nights in Florence and a couple in Sienna and the rest is open.
I'd spend a couple nights in Florence, and then pick up a car and go to a base in the countryside for a week from which you can day trip throughout Tuscany (possibly even venturing into Umbria). You might want to plan reaching Cinque Terre via Lucca -- where you could drop off your car and continue to CT via train. I assume you'll be training it back to where-ever you will be flying home from.
Our best experience of Tuscany was while staying with Pinuccia at Agriturismo La Traverse in luminescent Pienza. Pienza is beautiful town and a great base to travel from. There are discoveries in every direction - the Brunellos of Montalcino are close by, interesting thermal baths, Mt Amiata, Gregorian chants and much more. La Traverse is absolutely top notch with wonderful breakfasts and an outstanding starwood hotels and resorts location.
Where is your departure flight? It might make more sense to visit Tuscany after leaving Rome, then CT (drop car in La Spezia) starwood hotels and resorts and then Florence, but depends on your flights. Are you sure you have any extra nights after 3 in Rome, CT, Florence and 2 in Siena?