If you happen to be in Nebraska, Lincoln should be high on your list of places to visit. A few must sees I very much recommend are the Nebraska High School Hall of Fame, the International Quilt Study Center, the natural history museum, National Roller Skating Museum, the State Capitol and the Haymarket.
You should definitely check out the fossils exhibits with recreated mammoths, as well as the planetarium at Morrill Hall. Lincoln also has two large parks: Pioneers and Wilderness and visit the nature center and see the buffalo there. Nebraska Capitol offers free tours and on certain days you can tour the Governor's mansion as well. Other places worth checking are the sunken gardens, the Hyde Observatory and the Speedway motors historical car collection.
Not far from Lincoln you don't miss the Roca Berry Farm (in Roca) for fun hay rides, picking fruits and the outdoor maze which is quite cool. During Halloween they do a haunted event worth checking out. You can do also a mini wild safari at the Lee G. Simmons park (Ashland)