Fly into Venice and out of Rome, take trains going south to any one or two of these towns (among my favorites in Italy): Padua, Ferrara, Orvieto. These are only lesser known compared to Venice, Florence, and Rome, but they have wonderful walkable historic centers and great art and great food.
Ferrara and Padua are definitely less touristed than Orvieto. If you'd rather have fewer locations, Padua is an easy train trip from Venice, and Orvieto is an easy train trip from Rome. Ferrara can be an hour on the train from Venice, if you take the right train. Padua is not at all "small," but will give you that feel I think you are looking for, and has a terrific market, lovely piazze, and of course, the Scrovegni chapel.