With one day in Kake, you should visit the Kake Totem Pole, watch for fish, eagle and bear at Gunnuk Creek, and look around the historic cannery district. If a celebration is going on, join in to see the spirit of the community displayed through traditional food and dance, as well as entertaining games for all ages.
If you have more time in Kake, you could fly in and ferry out to experience the view from both air and from Keku Strait. In addition to seeing sights around town, staying longer allows for more exploration of Kupreanof Island. Rent a car and drive down the old logging roads that will lead you to various trailheads and wildlife viewing spots. Head out to Point White Junior Beach for whale viewing, up Hamilton Creek for fishing and bear viewing, or further out to Big John Bay to walk the mud flats and stay overnight in a remote forest service cabin.