Just got back from a trip to Tuscany. We spent a day + in Siena, an afternoon in Pienza and Montepulciano, a day + in Cortona, most of a day in Lucca, and 2 days in Florence. I would recommend all of it. Been to San Gim before, and that's also worth a visit. Stopped at, and liked Monteriggioni as well.

We also spent a day in Assisi and Perugia, which should be within day trip distance for you.