Since I live in Omaha, I feel obligated to represent.
If you are only here for a weekend and enjoy zoos, the Henry Dorley Zoo is a must see. It trades best in the nation yearly with San Diego depending on who opens a new exibit.
The children's museum is great for kids 3rd grade and under.
If you are interest in military planes, there is a large indoor "Air and Space" museum 15 minutes south of MA venue. They have flight simulators and other cool stuff for kids to do.
Just across the highway from the air and space museum, the zoo has a "wildlife safari" where you drive through spaces with animals like elk and buffalo and an area in the middle where you can get out and there is a petting zoo.
There is a recently built outlet mall with excellent stores like Underarmor, Polo, Micheal Kors (wife would appreciate last one) in the way from MA venue to the air and space museum. Lots of places to eat too.
Just 3 miles from the MA venue and hotels is the Kansas City Royals minor league AAA baseball team. They have a modern stadium with tons of stuff for kids to do--oh, and they also play excellent baseball.
Some people enjoy going to down town Omaha and visiting the "Old Market" with lots of local stores and excellent restaurants.
If you are a foodie, let me know and I will hook you up. Omaha has lots to offer besides excellent steak.
"And so ends this segment of Omaha – it's more than just a place to hold the pinewood nationals."
Eric