I have considered that but really want to follow the Oregon trail route just to get a feel for the history and see what the settlers went thru traveling west. Then see as many attractions as I can while making the journey out and on the return trip.Not sure what your budget is looking like, but I would consider looking into the cost differences with a fly and drive if seeing more is top of the agenda. Flight into Bozeman (close to Yellowstone) wandering around Yellowstone and Tetons for a week, then fly from Bozeman to Vegas (close to Grand Canyon) wander around Grand Canyon (arches etc) for a week, then back home would maximize time. Flights can be cheaper than you might think.
Now if the allure of driving across the country is the main allure of the trip, then that won't work. I get that allure, I had it, too, but that allure is growing less and less every time I drive across the middle...lol.
Just remember when planning drives, it's kind of like Alaska, things take longer to get to than what the map might tell you. You're gonna stop more than you plan, and find things to see you didn't know were there.
And stay off the interstates after you get west. Put the google map setting that says avoid highways, it will take twice as long to get where you want to go, but well worth the extra time.
Heck I do that even around GA and have taken routes I never knew were there.
The Redwood Forest in Calf. is nice as well. Then Glacier National Park in Montana. Also, Little Big Horn Battlefield. YelIowstone National Park in Wy. I second the gun museums. There are 2 in Cody Wy. Buffalo Bill and another one, can't remember the name. I took a day to go through both. Depending on the time of year you go, Wanenmacher's Tulsa Gun Show. Largest gun show on earth, really. 4000+ tables. If you can't find it, it just about wasn't made......There are other shows out west too.