Guess we could take a wild guess and assume your son is connected with the military. Since your son (and family) will be living in the area they are going to be a good resource for info..since its amazing how much you learn about a place in a short time. Many places in the area such as Pompeii and Herculanium can easily be reached by train or regional buses. Other places such as Capri, Sorrento, Ischia, etc can be reached by jetboat/hydrofoils. Not knowing Italian is not a major problem (we have spent many months in Italy including driving more then 10,000 miles within the country without speaking Italian) since many Italians speak and understand some English.
The one place you will need a car, be it a rental or a car/driver is the wonderful Amalfi Coast where you find places like Positano, Amalfi and Ravello. There are some excellent tour companies but it is quite expensive to hire your own driver/guide for a day unless you have a few others to split the cost. A full day tour can easily cost over 350 Euros. One highly recommended tour company is called Rome In Limo (Romeinlimo.com) and you can certainly look at their web site to get ideas. There are quite a few other reputable tour companies so you can certainly shop around. Although we understand you are visiting family in Naples you might want to consider spending a few nights in other parts of Italy. Besides Rome (already mentioned in another post) we strongly recommend visiting Florence and some of the surrounding area (Tuscany).