Alutiiq Museum is the best place in town to start if you want Kodiak to be more than scenery. Its exhibits cover thousands of years of Alutiiq/Sugpiaq life in the archipelago: archaeology, language, masks, tools, clothing, and contemporary work by Native artists.
The museum is small, but the subject is not. Visit before a wildlife trip or drive around the island and you will read the landscape differently, as homeland rather than empty wilderness.