Morril Hall on the University of Nebraska is good. It's a museum with all manner of ancient critters, mastodons, etc.
SAC museum 20 miles east of Lincoln at the 426 mile marker on I-80 is great to visit. It has airplanes up to and including a B52 and SR71 Blackbird on display.
During the summer, small towns around the area have annual firemen's picnics and ethnic celebrations. You can always have a good time at them.