Florence is connected to the north and south of Italy by the Autostrada del Sole (A1). It takes about 1½ hours of driving on scenic roads to get to Bologna (although heavy truck traffic over the Apennines often makes for slower going), about 3 hours to Rome, and 3 to 3½ hours to Milan. The Tyrrhenian Coast is an hour west on the A11.
An automobile in Florence is a major liability. If your itinerary includes parts of Italy where you'll want a car (such as Tuscany), pick the vehicle up on your way out of town.