The Union Pacific Railroad Museum in Council Bluffs is very well done - a small amount of self-promotion, and a bit of glossing over of some of the more unsavory parts of the past, but very engaging exhibits on the history of the transcontinental railroad and some good information on current train technology. The observation tower over UP's North Platte classification yard (a couple hundred miles west) is worth your time too. The Strategic Air Command museum southwest of Omaha is a great way to spend a few hours as well. Some rare aircraft, including a B-36 bomber and a British delta-wing bomber (can't remember the name) that's in their restoration hangar, along with more in-depth displays on the Doolittle raid, the Powers U-2 shootdown, and some other stuff. Omaha also features one of the few sites in the U.S. where a Japanese balloon bomb detonated (bonus points if you know the location of the only U.S. casualties from one of these), plus an original brick-paved section of the Lincoln Highway you can still drive (I'd recommend doing it slowly, however).