Zoo, space museum and Old Market by kingbk
Those are the three main tourist points here in Omaha. The zoo is supposedly one of the best in the nation. I'm not a zoo expert by any means, but it's worth stopping by at if your in the area. I honestly think some of the attractions are overhyped like the desert dome, but I do like the shark tunnel in the aquarium, the bridge in the creatures of the night section and the jungle is pretty neat, though many other cities now are starting to add them to their zoos. The zoo is hilly, so on a hot, summer day, it can get to be unbearable. They have all the other typical attractions as well, such as lions, tigers, bears, oh my!
The space museum is a far drive out, but it's something to do and it's only $6. It is easy to go through fairly quickly, but a good thing to explore if you like aviation or space.
The Old Market is the downtown district with shops, cafes, bars, restaurants and other things. It's a fun way to spend half of a day.