Things to do in Tuscany? - no car

You can visit the smaller villages by bus from Siena (e.g. San Gimignano, Monteriggioni, Pienza) or by train (e.g. Certaldo). Siena itself will keep you busy the best part of a full day.

There are plenty of places to go by train or bus in Toscana: Florence - 3/4days of course but also Carrara, where the white Italian marble to make Michelangelo's sculptures come from, San Gimignano, Montepulciano (wine), then there is the Isle of Elba (2 hours train or bus+ ferry to Portoferraio, capital of this small Tuscan island. There is also Livorno, San Gimignano, Saturnia, Porto Ercole, Talamone, Pitigliano, Pisa .....

Cinque terre might also be an option with a bus tour.

See bus connections summarized at the end of the Siena chapter in Rick's Italy book. For several destinations, you can see schedules at www.sienamobilita.it.