Located next to the historic Lyman Mission House, the Lyman Museum houses pretty good exhibits about Hawaiian and natural history. You can also take a tour of the Lyman Mission House itself, which has been restored and contains some of the original artifacts used by the early missionaries to Hawaii.

The ground floor of the museum has all of the Hawaiian history displays. You'll get a glimpse at how Hawaiian life evolved throughout the years--from Kamehameha's uniting of the islands, to the fall of the monarchy. One of the displays I remember most vividly is of ancient Hawaiian jewelry. They have a necklace made of human hair. The second floor of the museum has the natural history exhibits, including various rocks, minerals, and seashells. There are also some great photos of Native American and Hawaiian ceremony combined together for activities held on top of Mauna Kea.

Be forewarned this is a very small museum. Don't expect jaw-dropping exhibits. There's a lot of good information contained within, however, and it's a good way to spend a few hours in Hilo.