The Anthropological Museum of Father Sebastian Englert (a German missionary who came to the island to spread the good word and spent 35 years as parish priest, documenting its history, and particularly that of the stone inhabitants) is well worth a couple of hours (particularly if it's raining). Though it's basically just one large room, it's filled with interesting artefacts and information, particularly historical detail (and, it has to be said, some degree of speculation) about the islanders and the crafting and transportation of the statues, and geological background to the volcanoes and resultant stone used for the moai.
It also has several Rongo-Rongo tablets (the equivalent of the Rosetta Stone for the ancient Easter Island language and inscriptions, which, prior to discovery of the Rongo-Rongo stones, could not be translated), which are held in great awe and respect. Plus, I liked the only recognisably female moai statue (unfortunately broken in two), representing Ava Rei Pua, sister of Hotu Matua, the first king of the island and the museum exhibition speculates that there may be others, which were toppled and broken, even perhaps that they were targeted as female icons.
There's also an interesting section focussing on the statues' lost white coral ocular inserts -- wandering round, it had struck me that the faces didn't look alive, but the museum holds what is apparently the only example of a complete eye (with iris and pupil intact). No one knows why even those which were toppled but left intact were "blinded" by having their coral eye inserts removed or whether it is coincidental and they fell out when the statues were toppled and have since been lost. Curious.
In addition, there are numerous examples of tools and weapons, mock-ups of clothing and the usual figures stiffly sitting round a fake campfire, etc. More interesting is the series of comparative theories for the eternal "how were they moved?" conundrum and a topographical map of the country so you can get a feel for just how far some statues did have to be transported from the Rano Raraku quarry nursery to the shoreline.
Lastly, my favourite was a rather clumsy explanation/homage to Makemake, the birdman, explaining how the annual ceremony and competition took place, what the rules were (it's not apparent there really were any except to get back with the egg intact asap) and how the winner's sponsor then had to live as ruler for the year (which includes hairshaving and effectively living in seclusion -- not much of a victory overall?)
You can borrow excellent A4 photostat guides to the museum to use while you visit or, for US$2, it's worth buying to take away and use as you travel round and as a momento. The museum is located at Tahai (a short drive from Hanga Roa. It's open each day although opening hours seemed to vary without obvious reason. The curator is helpful and enthusiastic though his English is limited.
[P.S. If you want to read around the subject of Rapa Nuian artefacts such as Rongo-Rongo, I enjoyed Thor Heyerdahl's book Aku-Aku: The Secrets of Easter Island, which narrated his two year stay during the mid-1950s (before the airport was built -- he hired a Norwegian ex-whaling ship, converted it, and sailed down there via Pitcairn and Tahiti. On arrival, he tells of how he made friends with some islanders, met the good Father Englert and helped with his research and even erected one of the moai at Anakena, and occasionally gained access to inspect their secret caches of family goodies).]