I also like the Sorrento suggestion. Few crime worries there, and a very nice base for touring Naples, Pompei, Capri, Amalfi Coast and Paestum.

Updaate
 

They are leaning towards Sorrento, if they can find reasonably priced lodging.
They can stay in Naples for free (well, my points), but would only do that if they can't find anything in Sorrento.
They will definately visit the sights in the area.
Thanks for all the great advice!

Florence would be a much better choice if the Sorrento option doesn't pan out.

Even the Italians will tell you that Naples is not "Italy" - it's "Libya". It's amazing just how screwed up one place can be but that is Naples.

Btw, that tip about the buffalo mozzarella was spot on.

5 bucks says the Italians you were speaking to were "Northerners" ie. from Florence or north of it...

Naples isn't that messed up, IMO. Very different and chaotic and certainly not one thinks when speaking of Italy, but I think its a must see and do. There are far more "messed" up cities in Italy (in the south, that I have never been to), but tourists don't go to them.

Really, who were these "Italians"...?
That comment is absurd.

Napoli is fine, and if anyone has any measure of "street smarts" they will do fine in Napoli or any other Italian city. Some yahoo from a North American suburb might not get by, but any good "city slicker" will be fine.

There is much in Napoli and the whole region to see and do, and eat.

If the OP's woman are squemish or scarred, they should avoid most of Italia as there are pickpockets and crime in all the big cities, even in the north.

Ciao,
FH