Pompeii is definitely worth the train ride in my opinion.
Gelato, Gelato and more Gelato.
Watch out for groups of kids walking up to show you a newspaper or something similar. The little bastages will have even shorter kids sneak up and pick your pocket with your view blocked.
Do not buy any electronics from the back of a car, you will get a block of wood.
Somebody mentioned Naples. Armpit of the world. But I did get to meet Humpty Dumpty there on one trip. True icon.
An old Navy joke..... Why is Italy shaped like a boot? You can't get that much crap in a shoe.
All kidding aside. I think you will enjoy Italy. I spent time there on several occasions in the 80s and 90s. I think a tour guide in Rome is a good investment.