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I'd agree that I-80 to I-76 is the fastest route between the two cities. The trip can be made in two long days, or three pretty easy ones.
If you make the trip in 2 days, Omaha would be close to the half way point. If you stretched it into three you'd be looking at Iowa City or Des Moines the first night, with Grand Island, Kearney, or North Platte as second night stops.
I-80 is kind of the blue collar road of the American Interstates. It doesn't have the history of I-40, or the mountain beauty of I-70, but it is probably the most heavily used cross country route, particularly with truckers. That said, the journey does have its charm. There are plenty of good old fashioned small midwest towns in Iowa and Nebraska, particualrly in Eastern Iowa where the Amana Colonies and the Herbert Hoover Presidential Library are located.
The route does have some urban charm too. Omaha is a very underrated city with lots of things to do, and the Quad Cities along the Mississippi have a rich history as well.
Hope this helps you on your way!