Her's a route to consider if you can get lodging in Yellowstone.
Fly to Minneapolis (MSP). Rent a car there and drive to Rapid City, SD (about 9 hours). See Mt. Rushmore and Crazy Horse.
Leaving Rapid City, see Devil's Tower on the way to Yellowstone (via Cody). See Yellowstone using whatever lodging you can find or afford.
Leaving Yellowstone head north to Whitefish MT. (9 hours).
Leaving Whitefish drive through Glacier NP and end the day at Havre, MT. Leaving Havre, head for Bismarck, ND (state capitol). MSP is an easy days drive from Bismarck.
Fly home to Louisville.

<i>I also do not consider any of those places except Grand Canyon "out west".</i>

Everyone is entitled to his own opinion, but not his own facts.--Daniel Patrick Moynihan

Montana, Wyoming, Colorado, and New Mexico are among the Western States. Mt. Rushmore is about 40 miles from the Wyoming border. It is "out west" from where the OP lives, but it is not in a Western State.

HTtY

<i> It is "out west" from where the OP lives, but it is not in a Western State.
</i>

But it is west of the 100th Meridian, as per the post of dbdurand.