The Museo Archeologico Nazionale di Napoli - acronym MANN) Italian-language website.
English language website. On-line accessibily website.
IMPORTANT covid-crisis news: At this writing (Mid-Nov.'20) all museums in Italy are closed.
Many of them have on-line tours. MANN has one but it is sparse. You can try.
The National Archaeological Museum is located at the corner of via Foria and via Costantinopoli. That point was also the northwest corner of the original Greek wall of the city of Neapolis, remains of which can be seen further down via Costantinopoli at Piazza Bellini. It is a fitting site for one of the most complete collections of Greek and Roman antiquities in the world, and one of the few places where they can be viewed side by side just a few yards from precisely that outside world where they, indeed, existed side by side for centuries.
Charles III of Bourbon founded the museum in the 1750s. He used a building erected in 1585, one that had served as a cavalry barracks and later, from 1616 to 1777, as the seat of the University of Naples. Expansion of the premises continued in the latter half of the eighteenth century under the supervision of Ferdinando Fuga and Pompeo Schiantarelli. A final project drawn up in 1790 to complete the structure was never completed.
The museum houses
impressive collections from Pompei and Herculaneum; there are
exhibits from other archaeological sites throughout
southern Italy, including some from early non-Roman Italic peoples
of the area, such as the Samnites.
More recent additions include the Farnese
collection and the Borgia collection of Egyptian
antiquities, this latter giving the visitor the bonus of
studying the very real commercial and social ties
that the ancient Greek city had with its own
forerunner, Egypt. Other
collections contain items that in many other museums
would be considered much more than 'miscellaneous', such
as the 'Tazza Farnese,' one of the largest cameos in the
world, crafted in Alexandria in 150 BC and that came
into the possession of Lorenzo the Magnificent 15
[add - Jan 2012: The Staircase in the Entrance
Hall of the National Museum]