Some gentle reminders in case you're not aware of or forgot:
If your wife will carry a purse, make sure it's a cross body with durable material and a strong strap. I don't know if you guys like wearing a money belt or neck wallet type for deep storage of extra cash and cards and Passports.
Keep a big city awareness. You won't be chased down. Pickpockets like to tip toe in and tip toe out very fast.
Say, "No Grazie" to persistent street vendors or petitioners.
While on a train or bus, keep your bags in front of you. Don't want to tempt anyone. Never hang a bag on the back of a chair or placed on a table for an easy grab from someone. These are extreme examples, but why give them a chance?
If you're looking to tour some major attractions: Keep in mind - The Vatican, The Colosseo, The Borghese all require timed, entry tickets.
Papal Audience on Wednesdays - St. Peter's Square will be packed until about 1:00 -ish.
If you visit St. Peter's separately, there is no fee. There is a security check as with most of the major sites. No big bags or backpacks allowed - around 14" is pretty good. There is a checkroom at the lower level stairs near St. Peter's.
If you go to the Vatican Museums first, then you go through their security check and after the Sistine Chapel visit, you're led out to go directly to St. Peter's.
No bags at all at The Borghese. You would need to check one; some consider a money belt and leave the big bags in their hotel rooms.
The Pantheon is another gorgeous, active Church. There are guards sort of eyeballing bags and people. No entry fee is required; it may change by the time you go.
I can't speak on Naples, but, I would be extra cautious about bags, money, or walking around too aimlessly come nightfall.
I found Rome to be pretty safe. I had no fear or issues.
Update: I just saw your dates. So, if you want to tour any of the timed-entry sites, you may want to check on their official sites for tickets. The Borghese may be tough to get - they sell out very fast.