I had a very nice stay in Cortona this Spring. I picked it because it was easy to get to by train. It is about 2 hours from Rome and about 1.5 hours from Florence on the train line. You take the train to Camucia. From Camucia, you take a bus up the hill to Cortona (15 minutes). The main part of the town got a fair number of daytrippers, but was absolutely delightful in the morning and the evening. I went here directly after my flight to Rome and it was a great place to get over my jet lag.
Orvieto is another hill town that is easy to get to by train from Rome.
There are many great hill towns, but some are more challenging to get to by public transportation because the buses don't leave so frequently. There were frequent trains (every hour or two) from Rome that stopped in Camucia so this made it an easy place to get to when I first arrived. My flight arrived in the morning and I was in Cortona in time for lunch.