Wonderful area! This past May I spent 3 nights in Naples, then 4 nights in Sorrento, and enjoyed it all. In Naples I stayed at the WONDERFUL Orsini 46 B & B. Nice, quiet area convenient to various sites, and a healthy walk to many others all over town. I walked to the Museum and beyond, and the train station, without any problem. The building isn't much, but the B & B is lovely. It is a large apartment where the owners live in one part, and then there are three lovely rooms, very spacious and comfortable. Two of the rooms will hold 4 people each. The breakfasts are wonderful, brought to your room at the time you request. The owners are very nice and helpful, a youngish couple and their daughter who is about 10. Check out their really excellent reviews, one of the most highly rated spots in Naples, with very reasonable rates. With only 3 rooms, it might be hard to get a reservation though.
I spent one full day visiting the Museum and various neighborhoods and other sites in Naples. The other day I walked early through town to a market and then the central train station, then took a train to Salerno for a visit of a couple hours, then on to Paestum, which has three of the best preserved Greek Temples anywhere, including Greece. They are within some lesser ruins of a Roman town. Evidentally the Romans destroyed most of what they found, but respected religious sites and protected them. There is also a very nice modest-sized museum right by the ruins, for a very nice hour in the museum. The light for photos (and probably heat) in Paestum is best in the late afternoon. Since your son is interested in archeology and history, Paestum would be great because Pompeii etc. are all Roman, while Paestum is mostly earlier Greek, about 2450 years old. It is roughly an hour from Naples to Salerno, then 30 minutes more to Paestum.
From Naples to Sorrento, you might enjoy going by ferry more than the train. Or a private car or taxi will get you door-to-door in about an hour for about 100 euros, not bad with four of you. It was a splurge for me, just one person, but it saved so much time and energy moving with baggage, from inn to transport and then to another inn.
From Sorrento I went twice to spend days on the Amalfi Coast, once on a day tour, and then again by bus. Especially liked Ravello and Amalfi, not so much Positano, which was very crowded and commercial, even more than the others, and in June is probably moreso than May. My other day I went from Sorrento to Herculaneum and Pompeii by train. There, especially at Pompeii, I really recommend you latch onto to a guide by the entrance for a 2-hour guided walk. Talk to a few and choose one you can understand easily and who seems simpatico. I went on my own with a book and the RS audio tour, and I got lost a lot and missed things I only later found were really important and interesting. Pompeii is a really, really big and spread out site. A whole city, literally.
So, do it all, stay a long time, and eat delicious gelato and pizza at every stop. I especially recommend Fantasia Gelato in Naples, they have two or three locations.
