The area near Pompeii is unfortunately located in a very poor suburb or Naples. Just like in similar areas of America, these areas tend to be high in crime and gang related violence. When I rode the Circumvesuviana in 2007, I saw armed guards patrolling the carriages. Both the carriages and train stations were covered in spray paint graffiti, a reminder of the etymological origin of this word.
At the Circumvesuviana ticket widow, the attendant spoke only Italian. I struggled with the question, andata e ritorno? until the attendant drew a picture of two opposing arrows. At most other train stations in Europe, there was usually someone who spoke English.
While I never experienced or saw any crime, I was on high alert. Pompeii is worth the risk, but I would absolutely not go here after dark.
WARNING: Pompeii may not be appropriate for children because a highlight of the tour is a stop at several brothels around the city. Inside are frescos depicting available services. Although these areas can be bypassed, there is artwork scattered through the city that may not be appropriate for children. For adults, a good guide or audio tour is extremely informative of putting all this artwork into historical context, but it would not be understood by children.
-Paul