Four trips, all done in a day from the coast
The region is compact: you sleep by the sea and you see the cities.
The advantage of Tuscany is that you do not need to move base: from the Livorno coast or the Maremma you reach Florence, Siena, the Val d'Orcia and the Apuans in under two hours. All four of these trips are done by leaving the campsite in the morning and coming back in the evening.
Florence
An hour and a half from the coast. It is best to leave the car in one of the park-and-rides and take the tram, because the centre is a restricted traffic zone and the car parks inside are expensive. The Uffizi and the Accademia must be booked; the Duomo, the Baptistery and the campanile share one ticket. The rest is walked in a day.

Siena and the hills
Siena takes half a day: the Piazza del Campo, the striped cathedral and the town hall with the Good Government frescoes. In the afternoon you go down into the Val d'Orcia, where Pienza, San Quirico and Montalcino lie, or towards San Gimignano, which still has fourteen of the seventy-two towers it had in the fourteenth century.
Pisa and Lucca
They are twenty minutes apart. Pisa has the Campo dei Miracoli, seen in two hours, and the lungarni, which almost nobody looks at. Lucca has its sixteenth-century walls, walkable all the way round, four kilometres of tree-lined ramparts, and the Piazza dell'Anfiteatro, an oval of houses built on top of the Roman arena.
The Maremma and the tufa
From the Grosseto area you go to the Maremma park, with its paths through the scrub and its watchtowers, and carry on inland to the tufa towns, Pitigliano, Sorano and Sovana, built on rock cut by the Etruscans. Not far away are the thermal falls of Saturnia, free and always open.