Florence to Volterra to Orvieto

Without a car you should stay put in a city that gives you plenty of public transportation options. You should split your stay between Florence, Siena and Rome. From those 3 locations you can access buses and trains to see the rest (including Volterra and Orvieto). Basing yourself in volterra (or orvieto) without a car will limit your mobility options. Said this, I strongly encourage you to get rid of your fears and rent a car starting from the end of your stay in Florence. You would return your car in Orvieto (most agencies are near the Orvieto train station). From Orvieto you can go to Rome via train very easily. With a car you can easily base yourself in smaller towns, such as Volterra or many others. The car will increase your ability to visit more of the countryside and smaller towns and villages in both Tuscany and Umbria.

I agree with Roberto. I would not base myself in Volterra, it isn't really easy to get to or travel from. Great place to visit though. Orvieto is a maybe, but I would choose more nights in Orvieto than Volterra.

Volterra is small, but very relaxing. Three nights might be too much, but it's up to you. It's best to take a bus to Volterra (one change in Colle Val d'Este). I'd suggest returning to Florence and taking a train from there to Orvieto. This presumes you're content spending time in just these 2 cities. However, my recommendation would be 2 nights each in Volterra, Siena and Orvieto before arriving in Rome. Bus is your only option from Volterra to Siena, while train is you're best option from Siena to Orvieto (sometimes includes a bus from Siena to Chiusi).

We did exactly what you are planning. We rented a car at the Florence Airport, drove south thru the Chianti Country, actually stayed out side of Siena in the Village of Uoppini for one night then up to Volterra for the weekend. We left Volterra and drove to Montalchino, visited the abby at San Antimo and the small town of Pienza. Next day we retraced our steps to Montepulciano, spent a several hours soaking up the culture and drove to Orvieto, where we turned our car in. We stayed a few days in Orvieto at an wonderful apartment; then took the train back to Rome. It's a beautiful route and very easy to drive. If you want any of the accommodations recommends along the way private message me. I do not have accommodations in Volterra, as we stayed with family. I do have restaurant recommends there. Fred

With a car you can take day trips out of Volterra. San Gim is 20 minutes away. 2 or 3 nights is good. You can not drive inside the city walls of Volterra. There are convenient parking lots outside the gates. PM me and I'll ent you a few pictures of the place to peak you interest.

As usual, Roberto's 100% right. Tuscany is a region best seen by rental car. Roads are crooked, but well paved. It's very easy to navigate from city to city as road signs are well marked. I'd be bored to death spending 3 nights in Volterra without wheels. I could spend 2 nights in Orvieto as it'd give you time to see Civita.
I'd hate to see someone get so close to Rome and not take in the sights; even if it was for a couple of days. Rome's worthy of a 7 day visit, but the highlights really take 4 days.