May and September are the best months. The wheat fields below the town are green in May and gold in September, the wind off Amiata is cool, and the day-tripper crowds are smaller than in midsummer. June through August is hot, full and best avoided unless you can stay overnight and walk the town early in the morning before the buses arrive.
The first Sunday of September is the Fiera del Cacio — a pecorino-rolling festival in which competing teams chase wheels of cheese down a course around the cathedral. It is more entertaining than it sounds. Winter is quiet, very atmospheric in fog, and a good time to stay overnight if you can deal with shorter restaurant hours.