Forest Beekkeeper is correct. I did law enforcement there too. I second everything he said. Make sure you have cover plates on your very Italian, cheap car. Keep your electronics to a minimum and whatever you buy - break the boxes down and deposit them on base on out of the neighborhood. Nothing says rob me like an expensive TV box sitting next to the curb for trash pickup outside your house. We could pull around behind our house and unload out of sight. A roomate once unloaded a "toy" (stereo) after dark. We had a driveway and off the street parking.
What Beekeeper said is true - leave all your valuables in the states. Don't take your jewelry or grandma's silver with you. Leave them with a trusted relative or a safety deposit box.
We got robbed early on our first summer and I lost $150 worth of gadgets. My roomate lost $1K worth of gadgets. He also got in trouble by claiming he lost $4K worth of gadgets. The gov't would reimburse us back then (early 90s) like insurance if you had receipts to prove what was stolen or the amount (like mine) was really low. Today with computers and MP3 players and all that stuff I know an American home would be quite full of gadgets easily stolen. You certainly don't want a laptop sitting around with your financial information in it.
After we were robbed our landlord installed steel shutters and an alarm system. We tripped it off a few times (couple times per year) so the neighborhood knew we had one. We also had a couple of wonderful little mutt dogs. The tough part was finding them homes when my tour was over b/c my parents would not keep them for me while I finished my enlistment. Tough not because I couldn't find a home for them - but tough b/c I was very attached to them and they were very attached to me.
The last year of my tour my roommates and I could leave the doors open and leave. Between the dogs and the alarm system, nobody ever bothered us again. Dunno if coming and going in fatigues and with a gun belt made an impression on anyone. Probably not. We all had Italian "cover plates" on our cars so we looked like locals. We also did not put $500 stereos in our cars with prominent speakers in the rear shelf. Cheap speakers and cheap stereos that sounded pretty decent. My car (early 70s Beetle) was noisy anyhow so it wasn't like I was getting a recording studio quality listening experience anyhow.
When the summer rolled around the crime (thefts) went up - we took to hiding our rent money and a few higher priced gadgets inside cabinets. Our bookshelves would fold out into guest beds in the family room and we could open them and put valuables inside. How they opened was not obvious so I think a thief would move on rather than examine these cabinets. To do it again I might add a lock to the back to make it very difficult to open. A friend back then took his laptop to work with him (back when laptops were expensive and very lacking in capability). That way it was never home alone. It was safe to leave things locked in your trunk on base, not off base.
Today I could imagine modifying a cheap dinner table so the top lifts off revealing storage inside it. Enclose the area under the top. Add locks to the top won't come off unless a flush mounted desk lock is unlocked - that is pointing straight down inside the skirt (apron?) of the table. You'd want to create ways to protect what was inside the table so if the table was knocked over the contents did not rattle around too much. Perhaps put that laptop inside the mattress of a sleeper couch and close it up? Dunno if that would put too much pressure on the computer.
Be aware of how visible you are with your "wealth". Conspicuous wealth is not a good thing. Keep those gadgets away from 1st floor windows. Pass on that expensive stereo for your car. Like I mentioned before, dispose of packing materials away from home. Get to know your neighbors - American and Italian. We worked crazy alternate shifts so somebody was often at home. Our American neighbors were home at night (they had young kids) even if we weren't. We had noisy dogs that hated strangers.
The theft issues in Naples back then weren't any worse than I imagine they would be in any large American city. Thieves want easy things to sell to finance their bad habits. I never felt physically endangered by the locals as I wandered around and I went some crazy places at crazy hours - both on the job and off the job. As a parent now I cringe at some of the hours I was keeping back then...
We looked about as poor as our neighbors... Our neighbors were often pretty well off but b/c their homes looked iffy, the wealth was not obvious. I've looked at those places on Google Streets recently and noticed that many of the houses are now well painted and have sprouted air conditioners. The cars seem to have gotten nicer. The streets a little better cared for. It might be that the quality of life for everyone has improved a little so American lifestyle gadgets aren't as big a deal as they once were. When I lived there ('91-'94) my doctor friend bought their first microwave, their first VCR, and got cable TV. His car didn't have a/c in it despite being relatively new (Peugeot 406 TDI).
When you get there talk to your neighbors. Talk to your coworkers. Talk to American civilian base employees who have settled there. Have a talk with the military police shift leaders. Ask lots of questions about where they live, how they live, what their record for home theft has been like and what they can suggest.
Like several people on this forum have suggested - be sure to get friendly with your Italian neighbors. They can show you shops that might not be obvious as you drive through the neighborhood that you choose to live in. These shops can offer you real convenience over driving all the way back to the base to buy little stuff like hardware store stuff or food things.
Hope this was helpful info.