I lived in between Roma and Napoli and visited both cities very often. Roma because I loved it and Napoli because I had to. Crime in Italy, as most of Europe, is predominately no-violent. No matter where we found ourselves it was never scary to go out at night. Pick pockets abound in Roma, because of the tourists, as well as Napoli. Just make sure if you have a backback you stand against the wall in a crowd. Scam artists are very active as well, buy nothing from a street vendor.
I’ve gotta tell you, August is the WORST time to visit Italy. Many reasons chief is that it’s the busiest time for tourists. It’s hot stuffy and crowded. Everything in Roma from Piazza di Spagna (Spanish steps) to the Forum there are tourists just lounging everywhere, so many that it’s hard to walk around. August is the month that the bulk of italians vacation so all the beaches are super crowded as well. Just some friendly advice.
