I'll assume you have the big stuff taken care of.
If you're into religious art, there are several Caravaggio paintings in Rome. Most of them are in churches which are free to enter, I loved seeing those.
I think the Scavi tour in Rome is a must do.
Frascati vineyard, called Minardi, just outside of Rome is one of the oldest wine growing regions in Italy. They're a family owned multi gen winery that does unbelievable cooking classes with wine tastings.
Outside of Vesuvius and Pompeii there isn't a ton to do in Naples, but you're close enough to Sorrento to consider a day trip.
The best Gelato I had was in Assisi, Gelateria Leccapaletta Assisi. This is a great restaurant in Assisi: Le Terrazze di Properzio
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