The main museum for the island sits in Kärdla and covers Hiiumaa's natural and cultural history. The collection spans geology (including a solid display on the Kärdla meteorite crater), the island's Swedish-speaking community that predated the Estonian period, fishing and maritime traditions, and the Soviet occupation, which left a heavy footprint on Hiiumaa given its position near the Soviet western border.
The building is a modest 19th-century structure and the exhibits are well-presented. Allow a couple of hours. The staff speak English and are a good source of information on what to see elsewhere on the island. The museum is closed on Mondays.