If your children are into planes, spacecraft, and going to the moon, you should go to the Strategic Air & Space Museum.  They will get to get close up to fighter jets, bombers, and missiles.  

If you prefer a more peaceful theme to your family travel, perhaps you’ll like the Conservation Park & Wildlife Safari.  On the four-mile “safari,” you’ll get to see buffalo, deer, cranes, and other assorted animals.  While not exactly the most thrilling of safaris, its cost ($2 for young children) makes it worth the trip.

Don’t forget to spend a day at the Omaha zoo.  This zoo is absolutely stacked with everything from Gorillas to an IMAX theater.

The Omaha Children's Museum is great for the younger crowd.  There are plenty of hands-on activities, and the costs is quite reasonable ($5).

There is a seasonal water park called Fun-Plex.  Don’t get too excited, as this park is geared towards the little ones.  The rides are of the local church fair variety.  Still, if the day is hot, and your kids are small, they’ll certainly enjoy these tiny water rides.