The museum boasts that it holds the largest collection of material from classical antiquity in the world - it's not clear whether that's true but it certainly has more than enough to entertain for a good few hours -- hundreds of thousands including pieces from the Farnese collections such as the absolutely monumental sculptures of Hercules and the Farnese Bull, jewellery
(ground floor).
It's light and airy, thoughtfully laid out, signposted (you get a map in English and Italian with your ticket) and there are numerous assistants if you have a question (though woe betide you if you take a photo
with flash).
Of most interest perhaps are the numerous pieces brought for safekeeping from Pompei and Herculaneum (see entries below) (and lesser known Stabiae), including some quite breath-taking mosaics (mezzanine floor -- look in particular for the enormous mosaic of the handsome Macedonian leader,
Alexander the Great, astride his horse in mid-battle (hence "Battle of Alexander") shame really that it is not in situ on the floor of the Casa del Fauno in Pompeii but at least you can get up close now it's on the wall -- and the great, colourful scenes of fishes and squid/octopi, presumably used
either in a Roman kitchen or to advertise the wares of a Roman fishermonger?), some impressive and well-preserved bronze-works, on the first floor some impressive Roman frescos and paintings (Lord knows how they
got them off the walls), domestic furnshings and household goods.
Also look out on the first floor (room 94) for the excellent "Plastico di Pompei" - a scale model which will help you plan your trip or see where you've been.
So far as the mosaics are concerned, it helps I think to go to Pompei and
Herculaneum before coming to the museum so you can picture where the mosaics would once have lain -- conversely though seeing so many here makes you realise why perhaps the ancient sites are slightly less colourful that you might otherwise have expected.
There is also the material unearthed from Magna Grecia (Campagnoa and Southern Italy) such as the Vase of the Persians (first floor) and grave paintings from Cuma, Nola and Ruvo.
Admission 9-2pm every day save Tuesdays and Xmas/New Year's Days. Nearest underground is Piazza Cavour.