Besides southern Italy and it's historical significance, I've found more charming and interesting places in N.Italy.
Lucca is a charming renaissance walled city that I've found to be a nicer place to stay than Florence, food from the area I liked more than Florence and the weather was more agreeable. Florence may have more glitz but Lucca I thought had more character.
If you're more of a shopper or, enjoy indulging in some fashion shopping, consider Forte de Marmi. Along the Tuscan coast, north of Pisa but, South of Cinque Terre and a short train ride from Lucca, Forte de Marmi is the Santa Barbara of Italy. Well to do, Italians and other Europeans come here for their vacations, Wednesday is the Ladies Market where Italian fashion houses sell their excess and overages at a marked down rate. My g/f picked up some designer purse, she said normal price it would've been four digits, she said it was a deal...ok. The other girls picked up scarves, handbags, gloves and shoes. The guys, we just hung-out on the beach and drank spritz's at the cafe.
I spent some time in Bologna last year and I really enjoyed it. Being a foodie it was right up my ally but, there was more hang-out places due to the university vibe.
Ravenna should be at the top of second tier places to visit in Italy. The mosaics are impressive and a national treasure.
Ferrara is another walled city, just north of Bologna, like Lucca, it has a lot of character.
Further north, in the Dolomites is Cortina, a fantastic alpine village that is more Austrian/German in culture but, has that Italian vibe. In the winter it's a big ski vacation spot but in the Summer it's a great spot to get away from all the tourist hot spots and see a part of Italy that most American's don't consider. You can hire a guide and they'll take you on the variety of vie ferrate routes. The bigger city of Bolzano is another location to consider if you're looking for a bit more civilization, it's population is just over 100K so, big as far as mountain towns go. Still, it's apart of the Tyrol, which is nearly a separate country compared to the rest of Italy.