On our small group tours to Italy, we have gone beyond Rome, Florence and Venice to visit the real Italy.  Here are The Professor's favorite smaller Italian cities:

Padua:  Only 30 minutes from Venice, this is a haven from the throngs of people who visit the overcrowded city.  Padua has some great attractions in the Scrovegni Chapel, the largest piazza in Italy, the university where you can see Galileo's lectern, fantastic food, the Basilica of St. Anthony, Botanical Gardens, and the famous Cafe Pedrocchi.  On our Traveling Professor tours to Italy, we use Padua as our base because train transportation to other cities is so good.

Vicenza:  If you know who Palladio is, you know Vicenza. Evidence of his architectural style is evident in the Rotunda, the Teatro Olimpica and in buildings all over town.  Vicenza may be the wealthiest town in Italy and it shows.  It is small, relaxing, and fun.

Bassano del Grappa:  You've heard of grappa, and yes, Bassano is it's home, but the city is much more than that.  First of all, it is authentically Italian in that many shops still close for lunch.  Located in the foothills of the Dolomites, Palladio's Pont Vecchio crosses the Brenta River. Sit down and relax for a beautiful Italian lunch, as relaxing (and inexpensive) as can be.  Try some grappa and bring your camera.

Treviso:  We once rented an entire villa, grand piano and all, for about 100 euros a night.  It was glorious.  A mini-Venice we enjoy the fish market and dining in the romantic squares.