When my kids were little it was our favorite place to go. Hotels there are fairly cheap. They have a wonderful children's museum, riverboat rides, Funplex (a water park), Omaha Royal's games, and the Henry Doorly Zoo.
The Zoo is amazing. It has an indoor jungle...you can go through all 3 levels. It also has the Desert Dome/Kingdom of the Night. The upstairs in the dome is all desert animals. Downstairs it is dark...a bayou, an area with bats, etc. Then there's the Mutual of Omaha building with all it's hand's-on exhibits. Oh, and a building that has puffins, penguins, a walk-through tunnel aquarium, and lots of sea-life. Those are just the indoors exhibits...they also have a newwer gorilla house, bears, a carousel, an aviary, African animals, and a petting zoo. It's my favorite zoo ever...including the one in San Diego!
Our second favorite spot was the Twin Cities. St. Paul has a great children's museum, too. There's also Como park, the Paddleford riverboat rides (see a theme, lol?), the Minnesota State Zoo (moose, anyone?), and the Mall of America. My kids LOVED the Cheerio exhibit there...a whole hand's-on area devoted to breakfast cereal, lol! Last time we were there they had a play area where you could pay to have them watch your kids while you shop. There's a Rainforest Cafe there, bowling, movies, and hotels. All in the mall.
If you go, be sure to eat at Mickey's Diner...across the street from the children's museum. It's a classic!