If you take the above route, stop in Thermopolis and soak in the city's Hot Springs State Park Bath House (that's where the name comes from).
You probably already know, but Cody has 3-great Museums in one area that should not be missed called
The Buffalo Bill Center of the West.
https://centerofthewest.org/
If you are headed over to Yellowstone you'll travel through the Wapitii Valley, there is a State Park there on the Buffalo Bill Reservoir that's a good place stay.
Here's what it looks like: