It's my favourite, the one I always take foreigners to when they come. All in all, I've visited it maybe ten times in my life.
You'll find some archeological stuff here, but there's better in the Archeological museum. You don't come here for this. You come for the history of Greece from ancient times to the 19th century, through everyday and artistic objects: furniture, clothing, ceramics, embroideries, carpets (although the Islamic collection has been moved to the Islamic branch of the Benaki Museum, in the centre of the city). It even has two whole rooms moved here from Hepirus, with their carved wooden walls and ceilings. It is one of those places where you do want to read the plaques or to get someone to explain to you, because it takes a whole new life that way.
On the ground floor, there is a beautiful shop, but pricey. You will sigh in front of the replicas of the earrings in form of a ship in full sail. If you come to Athens, don't miss it.