Well, we get one whole day in Tuscany. Better than nothing Have rented a car and and want to do a day trip, concentrating more on the countryside and towns rather than the bigger cities. Can anyone suggest a nice route and places to see starting in Livorno? We'll arrive 31 October 0800.
Following the Via Aurelia in the direction of Grosseto - Roma, after 25 km you'll arrive at Bolgheri, where the famous Sassicaia wine is produced: and the small country is a bijoux. Or if you prefer, on the other direction (towards Pisa), you can go to Viareggio, Camaiore, Forte Dei Marmi, all very nice places to see.
In addition to the excellent suggestions and disregarding (per your comment) the bigger/touristy cities in range such as Pisa & Florence and if its nice weather then I would suggest a visit to the small towns along the cinque terre coastline, particularly "the bay of poets" where the poets Shelly and Byron stayed, in particular the towns of Lerici and Portovenere are very picturesque. If the weather's not great then Lucca is a nice inland town as an alternative to the obvious Siena. If you or other members of your party like designer goods/clothes you could hit the Gucci/Armani/Dolce Gabbana/Prada official discounted retail outlets just outside Florence. Take the A1 south for Rome, take the exit "Incisa in Valdarno". Turn right after the toll booth then follow the signs. One last thought - you could, just about, get to the Galleria Ferrari (Ferrari Museum) and back again in a day, although it would be a shame to spend most of your single day in a car! The Galleria Ferrari is closed on Sundays. Enjoy your cruise...