It is open from 9am to 7:30pm (except Tuesdays). A slightly cheaper way to see the museum if you also want to use local transport and see other sights, such as Pompei and the Herculanium, is the Naples Artecard (8€ to 25€, depending on the type).
The museum contains many of the best archeological finds from Pompei and Herculanium, including some impressive mosaics. The Egyptian section is not a must-see, though the open sarcophagi, complete with withered bodies, promise some grizzly viewing. The main attraction here is the Gabinetto Segreto, which is definitely well worth a look. It has hundreds of ancient '"curiosities" collected by Neapolitan collectors over the years. Artifacts range from the hardly noticeable at first glance to the somewhat more noticeable statue of Pan seducing a goat! Entrance to the exhibit is included with your ticket, but sometimes you must ask at the front desk for an allocated viewing time.