The mafia crime is generally not directed at tourists (They're too busy making money out of large-scale business and government corruption). There is a thriving and very large tourism industry in Naples, it's a great place to visit (Pompeii is nearby, you can catch a ferry to Capri or the Amalfi coast). It's also a beautiful city (albeit with a few problems from bad governance).
But if you're still worried tell them Tony Soprano sent you.
Phil almost 8 years ago
Petty crime is probably marginally higher then other big cities but if you are streetwise you'll be fine. Stick to tourist tracks and avoid backstreets/alleys as you would in NY, London or any other place in the world ... Don't miss Pompei before it falls apart and the coast with Sorrento, Amalfi and other gems. You can travel cheaply by circumvesuviana, a light railway system. I would also recommend a short trip to Caserta to visit the impressive Reggia (royal palace) and charming Benevento, the "witches" haunted place. almost 8 years ago