https://www.facebook.com/NorthForkOutfitting This place rents tubes and kayaks to float down the river in town. You can also rent paddle boats from them for cruising Sky View Lake or you can get bike rentals for biking along the Cowboy Trail.
Sunset Plaza Mall has a Target, JCPenny, nail salon, food court and a couple of other smaller stores to shop at. There is also a Walmart in town located at 2400 W Pasewalk, Norfolk, NE 68701
Omaha has one of the best zoos in the world. I would highly recommend visiting if you are going to be flying in and out of Omaha and are looking for something to do in Omaha.
There are a few golf courses around Norfolk: Fairplay Golf Course Eldorado Hills Golf Course Kelly's Country Club