...my first suggestion is: skip Nebraska.
I'd say try to hit Iowa, Nebraska and Kansas, just to be glad that you don't live in any of those states
I forgot which road it is, but I would skip I-25 (bad experience once) and go south through Utah and Arches National Park. Absolutely phenomenal. I don't know how possible it would be (been a
long time since I looked at a map for Utah), but hitting Zion and Bryce National Parks would leave you breathless.
Once you make it to I-40, make sure you visit the Grand Canyon (just between Flagstaff and Williams). When the sun is low, the rocks look like they are on fire. Unbelievable.
There is all sorts of things to see in the Southwest, it just depends on what you are looking for.
I-10 to LA is really, really boring for the most part though