The Musée de Normandie is an interesting museum that puts this popular region into perspective. And it's unique in that it has nothing to do with WWII, obviously a draw for millions of visitors.
The museum has several sections. First there is the Logis des Gouverneurs, which sits alone and dates back to the 14th century. In this building there are permanent exhibits tracing the history of Normandy back to the prehistoric ages and following through to various eras of migration and finally of the culture of the region. The Salles du Rempart takes visitors along the ramparts and shows not only Middle Ages items but archaeological finds as well. And the Exchequer's Room has items from the Bronze Age, the Iron Age, and other exhibits that portray the rich history of this fascinating region.
The museum is free for anyone under 26 years of age and on the first Sunday of each month. It is closed on Tuesdays from January through May and from November through December, and on all major national holidays. It should also be noted that many review websites confuse this museum with the Caen Memorial, which also has a museum.