Kodiak's main industry is fishing and evidence of this is everywhere you look. It's quite easy to walk to town from where the cruise ship is docked, and along the way there are interesting sights of fisherman and the fishing industry. Posted along one sea wall is a series of large displays that explain the fishing industry as practiced and experienced in Kodiak. You can see the posters HERE.
Once you arrive in town you'll find museums that explain the history of this region: the earliest settlers, the Russian influence (look for the dome of the Russian Orthodox church), and other cultural attractions. There's a good visitor center (I believe the shuttle bus from the ship's port terminates here) and helpful guides, maps, and pamphlets are available.