I love staying at this agriturismo in Greve (actually in the hills just next to the town): www.poggioallolmo.info
Your itinerary is very ambitious, by the way. Perhaps you might want to save some of the stops for another trip? One of the joys of being in the Tuscan or Umbrian countryside is finding time to explore, or to relax at a place you discover (rather than a place on an itinerary).
"Touring" the towns that you have indicated doesn't give you time to experience them. Maybe just the two nights in Cinque Terra and two nights in Florence (buy the Firenze Pass to make the most of your time!) and then add a day to Chianti region and to Montalcino.
While the distances are short on the map, traveling to Siena, for example, involves more time than you'd think, because just getting into the city is tough.
And definitely rent your car on your way OUT of Florence (at the airport -- there's a shuttle bus you can pick up at the main train station), because the city is a ticket-filled nightmare for drivers. Also, we followed Rick's advice and dropped our car off in Orvieto, taking the train into Rome, rather than driving to Rome. The airport, which is the most common rental car location in Rome, is a long drive from the city, but the train station is very centrally located in Rome, so you'd be better off. Orvieto's rental car (at least the Hertz) is open somewhat "Italian" hours, so check on hours of operation. If you do want to visit Civita, make sure to do so before you return your rental car in Orvieto -- while they are relatively close-by, they're not THAT close.
If you're looking for a wonderful place to stay in Montalcino, do check out Palazzina Cesira, by the way http://www.montalcinoitaly.com
Sandee (p.s. this is our third trip to Italy in 4 years, and we are just now getting to Cinque Terre -- you will find you won't want to leave the other places on your itinerary. Florence is lovely but very, very touristy -- I wouldn't have missed going there for the world, but it also was the only place in Italy I've felt taken advantage of. As a native Florentine from "outside the walls" (outside the walls of the city) explained, "inside the walls, all they care about is money."