I would recommend the northern route. That route will really show you the diversity of the country. Driving through places like Iowa and Nebraska can really give you an appreciation of what an incredible place the US is in terms of the different landscapes, lifestyles and people we have. There's nothing quite like emerging from the fields of Iowa into the martian landscape of Eastern SD. Or driving through Eastern Colorado and having that moment of "Is that a cloud or a mountaintop?" as the rockies peek over the earth's curvature. If this is a summer road trip stop in Walnut Woods State Park in Des Moines. Most incredible fireflies I've ever seen. It looked like the entire forest had been taken over by fairies :). Be sure to see the Great Salt Lake and the adjacent salt flats, too (yes, you'll probably see some mirages).

If you are looking for a road trip with long stretches of driving and wild and weird landscapes this is a good route to take. Also, I might try to tie in South Dakota on that northern route if you can... the Black Hills are incredible (Custer State Park has a massive bison herd and some of the best burgers in the USA) and you can check out Badlands NP on the way in. If you like cool hippie towns check out Asheville, NC just outside the smokies. One of the best beer towns in the USA and a seemingly endless amount of good food and drink there (PM me if you go there and I can throw some recommendations your way).

Overall, you can't go wrong! The other route will have you hitting New Mexico and Idaho which are both awesome (recommend Taos in NM and Boise/Sawtooth Mountains in Idaho). We have an awesome country and no matter where you drive you will find awesome people and places. The most incredible spots aren't always on a map :). Have an open mind and a great time! Feel free to ask away if you have any questions.