If you make it to Lucca in Tuscany, which has already been suggested, rent bikes and ride around the old city on the top of the walls(like a wide road). It is one of the only fully intact walled cities that was never breached. It gives you a chance to see the city in a way you can't from inside the walls. Very old as well, the Romans built on an Etruscan town before the early Italians. I think it was about 3 kilometers or so araound the city wall. Lucca is about 25 minutes drive inland from Pisa.
Assisi is really beautiful and highly recommended but is in Perugia several hours to a half day from much of Tuscany depending on whether you are in the north: (farther) Pisa, Lucca, Carrera; the middle--Florence, or father south--Sienna.
The good thing about your timing is that it is well before the tourist season which begins at the later part of June. We were in Florence right as the season was beginning and it was one of the worst tourist traps I have seen. Very crowded, noisy, the worst and most overpriced food in Italy. You have to make more of an effort there to get out of the tourist accomodations.
