Here is The Traveling Professor's list of favorite small and authentic Italian towns:

Bassano del Grappa:  Located at the foot of the Dolomites, a river runs right through this authentic Italian town, just one hour by train from Venice.  They still close all the shops for a lunchtime siesta here and travelers can have a lazy lunch on the almost empty, but beautiful squares at a fraction of the cost and without the frenzy of a place like St. Mark's Square in Venice.   I remember sitting down for a cocktail (only 4 euro) with a riverside view of the mountains in the background.  No waiting, no hassle.  It gets a 10 out of 10 on the relaxation scale.

Padua:  If you have been reading my blog posts with any regularity at all, you will know this is my favorite authentic Italian town.  Just 30 minutes from Venice and a world away in terms of crowds and trinket shops, there is plenty to do and see here like the Basilica of St. Anthony, the amazing Scrovegni Chapel (yes, it is BETTER than Sistine Chapel), 4 squares with markets and a whole lot of good, cheap, GOOD Italian eating spots.

Lake Garda:  Forget the Lake Como of George Clooney.  Don't battle the tourists or high prices but go to Sirmione on Lake Garda. The lake is larger than Como and more beautiful.  Just an hour from Verona.

Lucca:  Surrounded by two thick walls, now made into a walking/biking promenade, I don't think they have touched this town in 500 years.  Uncrowded on the weekdays and filled with Italians on the weekends, this small but sophisticated authentic Italian town is one of my favorites.  About 75 minutes by train from Florence.

Travel with The Professor on his small group tours to Italy.   Find out why over 60% of his travelers are return travelers.  Women travelers, especially women traveling alone are welcome on his small group tours.