Any places I need to stop and see between Michigan and Washington state?

Mt Rushmore and the Black hills. Avoid Wall Drug, I am sure you have seen enough drugstores in Mi to know what one looks like. If you are driving I-90, stop at the Chamberlain rest area. It has some beautiful views of the river, And after several hundred miles of flat, it is a dramatic pleasant surprise.

The Little Bighorn Battlefield.

Wall Drug!

Badlands National Park.

Rocky mountains…....

Hampton Inn has this quirky landmark site. It might be worth checking out.

That is a very wide open question. It all depends on how much time you have, and what you like. The very best single answer is, allow at least three days for Yellowstone National Park. Wall Drug is not worth exiting the freeway for. If you really have six hours to kill, Mt. Rushmore becomes… ahhh, OK, I saw it. I wouldn’t do it. Instead, use the six hours to see Badlands Park, but only if you reserve the three days for Yellowstone. Enter Yellowstone through Beartooth Pass, NE entrance. It is spectacular. Best accommodations, Old Faithful, if you can get it. Second best accommodations, Grant Village. Don’t miss The Yellowstone River Canyon, spectacular.