Ronald, 4 days may be enough but that depends on what all you want to see and do.
Some of the "Must see" places are Pompeii, Ercolano, maybe climb Vesuvio.
When you go to Pompeii, you can take the train from the Central Station. Pompeii is very large and I would suggest taking a guided tour, there will be plenty of tour guides to meet you after you buy your ticket. The larger the tour group the less it will cost per person. The tour will last about one hour to an hour and a half. They also have self guided tours. After the tour you can explore on you own.
I prefer Ercolano because it is a bit smaller and better preserved. If you want to climb Mt. Vesuvio, you can catch the bus up the mountain. once you get off the bus, you have to climb a very steep slope, it shouldn't be any problem for a young man like yourself. Climbing the mountain is free until you reach a certain point. If you want to see the crater then you have to pay. I used to be about 5 euro to go the rest of the way. If you're going to climb that high , you might as well pay to see it.
That should take up a whole day. If you really want to see the relics from Pompeii, you have to go to the Museo Archeologico Nazionale, this is where they keep all of the neat stuff they collected from the ruins. They even have a special room for all the porn that they found!
While you are downtown, you should also visit the Capella Sansevero and see the Veiled Christ. It is one of the most amazing sculptures you will ever see!
There are several Castles to see, one the most famous is the Mashio Angioino (my wife loves to say that name) or the Castel Nuovo. You can also see the Galleria Umberto, very famous architecture.
Check out
Http://goitaly.about.com/od/naples/a/naples.htm this site has some very good tips on buses and trains and sites to see.
If you can find "Food and Wine Guide to Naples and Campania" by Carla Capalba, get it! You can get it on Amazon . It has some very good ideas about the area.
If you are going to use the local transportation, just be aware of pickpockets. I sense that you have been using it up north but it may be a bit different down south. Garibaldi is the central Train and bus station in downtown Naples. Beware of the thieves there also, sort of like the station in Rome. You can get a train to POmpeii and also down to Sorrento. Sorrento is a great place to walk around and hang out. It's where they make Limoncello and you can get free samples in several places. Stop in La Boteggucia and say hello to my friend Jasmina. She owns a very good Intarsia store.
Capri is okay but very expensive, I would rather go out to Ischia. It is a bigger Island and more laid back and less touristy. Capri and Ischia would be a whole day trip.
The food in the Campania region is the best, like Ed said. If you like seafood, try Spaghetti con Vongole, insalata mare, of course the mozzarella is to die for ( my wife thinks that's what caused my
heart attack!)and the bread is so much better in the south , try to find pane cafone.
Okay that 's enough for now. I'll look back over this and see what else I can add later. If you go to the thread on Campania and you will see some sites that Villa has added.
Ciao for now,
Dan