I agree that you won't want to be changing lenses in the great outdoors where dirt, sand, dust, and moisture can be unavoidable, and do you really want to be stopping and changing lenses very often? My guess is you'll find the 17-70 the most used lens. Most of that area is truly wide open spaces and big skies
I just came back from a trip out west, Colorado, Wyoming, and South Dakota. During the two weeks with my K-5, the two most used lenses were a 17mm Takumar in almost every state, and an older SMC-A 28-135mm at Crazy Horse Monument and Mount Rushmore.
My Daughter used the DA 55-300 on her K-30 during the trips to Custer State Park and the buffalo herds. The funny thing was, several of the herds were right next to the road, so she didn't need the zoom very often.
The 21mm and the 40mm are good mulit-purpose lenses, and only take a small amount of room, so they almost always go in my bag, just in case.
As a planning note, you might be tempted to take the western approach to Mount Rushmore if you are coming from Wyoming, but I'd encourage you to take
Route 16a The Iron Mountain Road, because it has several views of Mount Rushmore at a distance that you can't get from any other road, including a few tunnels that frame the Presidents as you drive through them towards the park itself. Also,
the Crazy Horse Memorialis not far from Mount Rushmore and is even more incredible a sight. All of the presidents at Mount Rushmore can fit in the area composing head and hair of Crazy Horse, it is a magnificent sight! The good thing about that area is you can see more than one attraction in a day, we stayed in Hot Springs rather than Rapid City, it was a nice little town with a few sights of its own, and good restaurants. Stop at Wall Drug on your way to the Badlands, it's actually a cool place to check out and shoot pix, and the Badlands is certainly worth seeing, it will remind you of the Southwest, but it has some differences as well.