Naples doesn't ease you in. The first hour is scooters coming at you from three directions, washing hung across alleys, church bells, shouting, and someone pressing a coffee into your hand that's stronger than anything you've had before. Most visitors decide in that hour whether they love it or want to leave. Stay. Naples is one of the oldest continuously lived-in cities in Europe: Greeks from Cumae laid out its street grid around 2,500 years ago, and you still walk on it. After them came Romans, Normans, Angevins, Aragonese, Spanish viceroys and Bourbon kings, and for a long time it was one of the biggest capitals in Europe.
It's a city of layers, in every sense. Under the street there are Greek cisterns, Roman theaters, early Christian catacombs and World War II shelters, and above it baroque churches with more marble than seems possible. Between the two, people live at full volume. Football is a religion here, the patron saint's blood is expected to liquefy three times a year, and everyone has an opinion about which pizzeria is best. Five days is the right amount: enough for the city itself, plus Pompeii and Vesuvius, without rushing.
This plan keeps each day in one part of town. Day one is the historic center and underground Naples, day two the Archaeological Museum, the Sanità district and Capodimonte, day three royal Naples, Via Toledo and the view from Vomero, day four Pompeii and Vesuvius, and day five the castles, the seafront and Posillipo. Herculaneum, Capri, Procida and the Amalfi Coast come after day five. Because so many museums close on Tuesdays and Wednesdays, the plan works best if day one is a Thursday. For the bigger picture, see our page on Italy.