I just got back from nine days in Naples.
Pompeii is incredibly crowded, with tourists, tourist groups, and children on field trips. I'm glad I went, I would've regretted it if I passed on it, but I learned more about Pompeii at the incredible National Archeological Museum — where there's breathing room and time to take in what I was seeing — than in Pompeii. The Museum had a good crowd, but I found myself many times virtually alone in rooms. The line for tickets moved quickly enough.
The Capodimonte is a must for anyone interested in art. That museum, too, gives you plenty of elbow room. The adjacent park is lovely. Another must is the Monte della Misercordia, which houses Caravaggio's Seven Acts of Mercy; this church is conveniently near the awesome Duomo.
Meals in Naples are shockingly inexpensive compared to, say Venice or New York City. Excellent pizza, real pizza, is four or five euros. Linguine and clams, a favorite of mine, is ten or twelve euros and it's the real thing; it is at least twice that in NYC, where they still don't quite get it. You have to have the right clams or you blow it. A full bottle of good wine is nine or ten euros. If you get a single glass, they give you a generous pour.
I stayed near the train station at Hotel San Pietro (highly recommended) and ate twice at Da Donato, twice at La Cantina dei Mille, and twice at Mimi e Ferrovia. I ate a pizza margherita at the fabled L' Antica Pizzeria da Michele. You take a number to get in but everything moves fast. I have to say I was somewhat disappointed; the pizza, at least for me, wasn't quite baked through, and the bottom was somewhat doughy.