Jennifer,
As you're planning on renting a car, note that each driver listed on the rental form will require the compulsory International Driver's Permit, which is used in conjunction with your home D.L.'s. These are easily obtained at any AAA office for a small charge, and are valid for one year.
Be sure to do some research on the dreaded ZTL (limited traffic) areas which exist in many Italian towns and cities these days. EACH pass through one will result in hefty fines, which you likely won't know about until you return home. Do NOT drive in Florence (if you were planning to go there) as the city is just about saturated with automated ZTL cameras. You'll also need to be vigilant to avoid the automated speed cameras and the Traffic Tutor system on the motorways which not only measures instantaneous speed but also average speed between two points. Exceed either one and tickets with hefty fines will follow. In addition to the amount of the fines, you'll also be paying the rental agency a processing fee for providing the authorities with your name and address.
As the others have mentioned, unless you're going to be travelling to smaller towns not well served by public transit, using the trains is a much easier and quicker method of travel. The high speed versions travel at up to 300 km/h which no car can match, so that's a more efficient use of limited travel time. Using the trains means you won't have to limit your hotel choices to only places that have easy parking and are located close to an exit. Which method of transportation to choose will depend on the specifics of your trip, and without a more complete picture, it's difficult to provide specific suggestions.
In any case, hope you have a wonderful trip!