Yes you can, provided you don’t choose Montepulciano and Pienza, two of Rick Steve’s’ favorites but which cannot be visited efficiently without a car.
You just need to choose a base that is a transportation hub for the area. Basically Florence or Siena.
Since you are coming from afar, you should probably settle in Florence, which is Tuscany’s capital and transportation hub of Tuscany, and quickly reachable by high speed train from Naples. Lots of Tuscan towns can be visited from Florence via bus or train.
Another option is to settle in Siena, which is the provincial capital of the Province of Siena. Siena itself is a gem to visit, but also from it you can visit many small towns nearby by bus, like San Gimignano, Monteriggioni, Buonconvento.
Getting to Siena requires a bit extra time. Coming from Naples the fastest way is a high speed train to Florence then a 75 min bus ride (or 90 min train ride) southward to Siena.