Some Napolitano friends recommended a place when we went to Naples last year, and we ended up going back twice. I think it goes by two different names: I Masanielli, or just Masaniello. It's on the Riviera de Chiaia. The antipasto platters are huge and delicious; the seafood was excellent. The owner is very American-friendly - ask him what he suggests that day.
If no one has mentioned to you already, keep in mind that the desserts aren't so great at the restaurants. Better off having a meal then going to a pastry place for dessert.
We also liked 53, on the Piazza Dante.
If you need a quick afternoon shot, Mexico has good coffee. People love the pastries at Scaturchio, and they were good, but I liked the ones at the stand in the Galleria better.
Naples last week for my wife and I was terrific. Here are the gems: Da Ettore on Santa Lucia, Dora, Umberto, Mattozzi Europeo, and Trattoria da Cicciotto in Posillipo. If you can sing an aria, then Dora is the best. These are all small family restaurants and outstanding. Did not like Brandi the famous pizzaria. Hotel Palazzo Alabardieri is one of the finest I have stayed in anywhere and a perfect location.
In Sorrento Rist."La Favorita" O'Parrucchiano is beautiful and excellent.
i fell completely in love with naples when we were there last year. i simply could not get enough pizza and must have eaten it every day for lunch.
fave for me (but this is always teh subject of MUCH debate) was di matteo, via tribunali, 94. rough and ready, but seriously the best pizza i have ever had. plain margherita was th way to go for me.
also good are old standbys -
brandi, salita sant'anna di palazzo, 1.
da michele, via C. sersale, 1.
we also had a good pizza at ciro a mergellina, via mergellina, 18/21
naples rocks. seriously, i absolutely LOVED it. so much wilder than the rest of italy. just more sass and personality.
parts appear dodgy, but act sensibly and keep your wits about you and you'll be duly rewarded.
Scour this site for discussions about the classic pizzerie--da Michele, Ciro, Bellini, Port'Alba. Make sure you hit some street markets (Pignasecca, for one-just up off via Toledo, Forcella), eat street foods (calzone, sfizzi, or fried snacks of innumerable kinds), and focus everywhere on great seafood and fish. Pozzuoli, a rough and ready seaside town about a 30 min commute by subway (home to Sophia Loren) for even more waterfront color--many simple seafood trattorie for very fresh traditional dishes. For dessert,Pintauro as well; everywhere, try pastiera (ricotta pie) and sfogliatelle. Good local wines from Campania, of course--from Greco di Tufo whites to Piedigrosso and Aglianico reds. Finally, for a quick detour, a boat to the near-in island of Procida for the day. Have a great time.