Naples gets a bad rap.
When I first moved to Rome I listened to a podcast that advised "if you love Rome, head further south. If you don't love Rome, start planning Tuscan and alpine adventures. I used to think that was good advice. I have changed my mind. Now I think that everyone should visit Naples.
"Take the energy of New York, mix in the gritty elegance of New Orleans, add 3,000 years of history, and cook it all up in the heat of the world's most famous volcano -- that is Napoli."Stanley Tucci, Searching for Italy
Naples is an easy day trip from Rome. The train ride takes just over an hour. Or a perfect stopover before or after an Amalfi Coast (or might I suggest the Cilento?) trip.