Downtown Omaha has some restored historic buildings and a lively area with restaurants and bars. I think the area is called Old Market. There are also a couple museums, IIRC one art and one history but a bit more unique.....There's a new Hyatt Place so you could look on their website for suggestions of things to do and see if you don't want to start with a normal google search.

Don't forget that Omaha was at the center of the movie Up in The Air.