Ciao John,
Many areas in Tuscany can be visited with public transportation, but with some it isn't very convenient. For example, both Chianti and Val d'Orcia do have buses (there are no train tracks crossing them) that service the area, but schedules are not very good overall so a lot of time is wasted. So if you really want to visit these areas, a rental car is definitely recommended.
Then it really depends on where you'd like to go. The best next step to take would be to decide whether you can visit the places you want to visit with public transportation OR to visit places that can be reached with public transportation. An itinerary that CAN BE done without a car rental would include Florence, Pisa, Lucca, Siena and San Gimignano. Depending on the time of year you visit, you can also reach the sea coast by train, like Viareggio and the Versilia.
Hope this info is useful in planning your trip!