Sifracar, a local franchise of Hertz, will be the easiest if not the most economical way to get from the port of Livorno to Lucca, Pisa, San Gimignano, Volterra, Florence or any one of a number or combination of towns in Tuscany. they will be waiting on the dock, immediately in front of the ship , with your car, ready to go. You return the car directly to the dock when finished, couldn't be easier. At about 90 euros for the smallest car, it is not cheap but certainly convenient. Price includes: unlimited mileage, tax, basic insurance and delivery/collection to/from the port. For an additional fee of about 10 euros they will include a GPS unit pre programmed with routing to all the local towns, including parking info.
Last summer we gone to Croatia and Italy. After Dubrovnik (Croatia) and Split the pest place on this travel was Livorno.
At Dubrovnik Airport we rented a car at Kompas Rent a Car (www.kompasrent.hr) and we returned it in Venice airport. We had Renault Clio. Very nice car for economy price.
>>>>>>>>>>> By Train
The Arno valley line runs 24 trains daily from Florence (about 1 1/2 hr.) through Pisa (14 min.) to Livorno Centrale (tel. 0586/400-456), where you can catch the no. 1, 2, or 8 bus (and many others, though they don't make a beeline) to Piazza Grande in the center of town .
There's a highway from Florence that runs straight into town. From Pisa, the fastest way is to zip down the SS1. Convenient pay parking is along the Fosse Reale, on Via Magenta, and on Viale Carducci.
Lazzi buses (tel. 0586/899-562) run from Florence and Pisa to the Livorno terminal at Piazza Manin on the Fosse Reale, just a hop away from the tourist office on Piazza Cavour. ATL buses (tel. 0586/884-262) run from Piazza Grande to service Pisa and Livorno's province down the coast, including Castiglioncello, Cecina, and Piombino
Livorno is a big city full of motorcycles and cars, so if you really want to move to another place in few minutes, the best way to do it is to wait a bus. They are almost 5 bus a hour (and in Italy this is not always easy to find!) to go everywhere in Livorno and outside.