How about pizza? Some of the great pizzerie are not open for lunch (the ovens are not yet hot enough), but one that is, if you're in the area of Spaccanapoli is:
DI MATTEO
Via dei Tribunali, 94
At least, when we were there, they also had their version of a slice, if you're in a hurry. And you might be, because just a couple of blocks away at Piazza S. Domenico Maggiore, is Scaturchio where you'll find the gold standard in sfogliatelle.
Altho if it's a nice day and you're by the bay there's nothing much better than an al fresco spaghetti alle vongole in a number of restaurants overlooking the bay. (My favorite has unfortunately closed.)
One other thought is a restaurant called, I believe, La Tavernetta (?) which I've never been to but which the NYTimes, based on a recent article I haven't saved, apparently thinks is the best value euro-for-euro in Naples and is open only for lunch. You'll have to do some searching to find more info about this one, but it sounded like it'd be worth the effort.
One further bit of advice, don't get suckered into going to Brandi's which may have served good pizza in Queen Margherita's day, but is now fairly tourist-ridden.
"The fork with two prongs is in use in northern Europe. In England, they’re armed with a steel trident, a fork with three prongs. In France we have a fork with four prongs; it’s the height of civilization." Eugene Briffault (1846)