Hey there! Italian, currently living in Italy (with US husband)! Love this thread
Lesser-known places in Italy that are totally worth visiting:
Bologna / Modena - Emilia Romagna region (art, food, Ferrari)
Comacchio / Ravenna Emilia Romagna region (coastal towns, Comacchio is also called Little Venice)
Perugia / Gubbio / Assisi - Umbria Region
Genova and the Ligurian Riviera (If you saw Luca - the Pixar movie, you know

)
The Garda Lake region and the town of Arco, if you are into hiking, climbing, fresh mountain air
San Marino - well, technically not even Italy! San Marino, it's another Country in Italy and totally worth exploring!
Those places are actual little gems, worth exploring if you're planning to visit more known destinations such as Venice, Florence, or Rome. It's where the Italians go on family, long weekend trips. Also, I only pointed out north and central Italy places, as I'm not very familiar with the south.