It's only fitting that the Museo Archeologico Nazionale—the single most important and remarkable museum of Greco-Roman antiquities in the world (in spite of itself, some observers say)—sits in the upper decumanus, or neighborhood, of ancient Neapolis, the district colonized by the ancient Greeks and Romans. Happily, it's open all day (its core collection, that is). But if two hours are your limit for gazing at ancient art, nearby you can discover some of the lesser-known delights of medieval and Renaissance Naples, along with the city's lush botanical gardens. Along the way are churches that are repositories for magnificent 15th- and 16th-century art and sculpture.
If you're feeling intrepid you might like to deviate into La Sanità, one of Naples' most densely populated and uncomfortably lawless neighborhoods, still studded with legendary palaces and gilded churches as well as the fascinating Cimitero delle Fontanelle.
The Parco di Capodimonte is the crowning point of the vast mountainous plain that slopes down through the city to the waterfront area. Nearly 5 km (3 miles) removed from the crowds in the Centro Storico, it is enjoyed by locals and visitors alike as a favored escape from the overheated city center. With picture-perfect views over the entire city and bay, the park was first founded in the 18th century as a hunting preserve by Charles of Bourbon. Before long, partly to house the famous Farnese collection that he had inherited from his mother, he commissioned a spectacular Palazzo Reale for the park. Today this palace is the Museo di Capodimonte, which contains among its treasures the city's greatest collection of Old Masters paintings.