Just a couple of quick ideas off the top of my head. We've been to Italy almost every year for the last 10 years, and never went any place we didn't enjoy.

Once we did a two week excursion to Le Marche (the Marches), but you need a car (we started in Bologna). Absolutely fabulous, it's like Tuscany but no tourists. Urbino is especially worth a visit.

There's a series of great cities along an easily accessible train line: Parma, Modena, Bologna, then on to Ravenna. Great food and art in all of them.

Verona, Padua, and Mantova are all wonderful, medium size cities worth visiting.

From Rome, take a train to Perugia, then from there take the narrow gauge train to Sansepolcro. Arezzo is a short bus ride away. (This is for anyone interested in paintings by Piero della Francesca.)

In any of the places above, you'll be shocked at the relative lack of tourists compared to Venice and Florence.