Naples was a capital of a country. Nearby there are Ercolano, a ruin from the antiquity, the Mount Vesuvius which swept away Pompeii in 79 AD, Pompeii itself which is about 20 minutes by train from the mountain, and the impressive Royal Palace in Caserta, 45-50 minutes by train from Naples. All these places deserve to be visited. Ercolano, Mount Vesuvius and Pompeii can be visited in a one-day trip by one has to hasten. One day should be spared for the Royal Palace.
Insider Tip:Try the pizzas at the old-town pizzerias. They are huge and tasty.