Built by the Normans in the 12th century, Naples’ oldest castle owes its name (Castle of the Egg) to Virgil. The Roman scribe reputedly buried an egg on the site where the castle now stands, warning that when the egg breaks, the castle (and Naples) will fall. Thankfully, both are still standing, and walking up to the castle's ramparts will reward you with a breathtaking panorama.

Used by the Swabians, Angevins and Alfonso of Aragon, who modified it to suit his military needs, the castle sits on the rocky, restaurant-lined 'island' of Borgo Marinaro . According to legend, the heartbroken siren Partenope washed ashore here after failing to seduce Ulysses with her song. It's also where the Greeks first settled the city in the 7th century BC, calling the island Megaris. Its commanding position wasn't wasted on the Roman general Lucullus, either, who had his villa here long before the castle hit the skyline. Views aside, the castle is also the setting for temporary art exhibitions, special events, and no shortage of posing brides and grooms.

The high point (quite literally) of the Neapolitan baroque, this charterhouse-turned-museum was founded as a Carthusian monastery in the 14th century. Centred on one of the most beautiful cloisters in Italy, it has been decorated, adorned and altered over the centuries by some of Italy’s finest talent, most importantly Giovanni Antonio Dosio in the 16th century and baroque master Cosimo Fanzago a century later. Nowadays, it’s a superb repository of Neapolitan artistry.

The monastery’s church and the rooms that flank it contain a feast of frescoes and paintings by some of Naples’ greatest 17th-century artists, among them Francesco Solimena, Massimo Stanzione, Giuseppe de Ribera and Battista Caracciolo. In the nave, Cosimo Fanzago’s inlaid marble work is simply extraordinary.

Adjacent to the church, the Chiostro dei Procuratori is the smaller of the monastery’s two cloisters. A grand corridor on the left leads to the larger Chiostro Grande (Great Cloister). Originally designed by Dosio in the late 16th century and added to by Fanzago, it’s a sublime composition of Tuscan-Doric porticoes, marble statues and vibrant camellias. The skulls mounted on the balustrade were a light-hearted reminder to the monks of their own mortality.

Just off the Chiostro dei Procuratori, the small Sezione Navale documents the history of the Bourbon navy from 1734 to 1860, and features a small collection of beautiful royal barges. The Sezione Presepiale houses a whimsical collection of rare Neapolitan presepi (nativity scenes) from the 18th and 19th centuries, including the colossal 18th-century Cuciniello creation, which covers one wall of what used to be the monastery’s kitchen. The Quarto del Priore in the southern wing houses the bulk of the picture collection, as well as one of the museum’s most famous pieces, Pietro Bernini’s tender Madonna col Bambino e San Giovannino (Madonna and Child with the Infant John the Baptist).

A pictorial history of Naples is told in Immagini e Memorie di Napoli (Images and Memories of Naples). Here you’ll find portraits of historic characters; antique maps, including a 35-panel copper map of 18th-century Naples in Room 45; and rooms dedicated to major historical events such as the Revolt of the Masaniello (Room 36) and the plague (Room 37). Room 32 boasts the beautiful Tavola Strozzi (Strozzi Table); its fabled depiction of 15th-century maritime Naples is one of the city’s most celebrated historical records.

You will need to book in advance to access the Certosa's imposing Sotterranei Gotici (Gothic basement), open to the public on Saturday and Sunday at 11.30am (with guided tour in Italian) and 4.30pm (without guided tour). The austere vaulted space is home to about 150 marble sculptures and epigraphs, including a statue of St Francis of Assisi by 18th-century master sculptor Giuseppe Sanmartino. To book a visit, email accoglienza.sanmartino@beniculturali.it at least two weeks in advance.

One of the best spots to chill with a spritz is this free-spirited, bar-lined square. Featuring excavated ruins from the city's 4th-century Greek city walls, it's the classic go-to for bohemians and best experienced in the evening when it heaves with uni students, left-leaning crowds and a healthy dose of flirtatious glances. Generally speaking, bars at the western end of the square attract the bulk of locals, while those on the eastern side draw the out-of-town crowds