If you are planning day trips from Siena to the hill towns in the surroundings, renting a car is the way to go.
The other option you have, transfer by bus, will limit the number of towns or places a day you can visit.
If you are not afraid of driving there — driving there is easy if you use common sense driving habits — in a couple of days you could visit the major places in the surroundings.
Strongly suggested the following hill towns: San Gimignano, Colle Val d’Elsa, Volterra, Certaldo, and towns located along major wine roads such as Montalcino, Pienza and Montepulciano or in the Chianti area: Castellina in Chianti, Gaiole in Chianti, Greve in Chianti and Radda in Chianti. (See map of Chianti area and countryside of Tuscany).