Boiling River is another good little gem if going through the park in my opinion. Going through Beartooth is scenic as well, though COVID did a number on the shops in Red Lodge. Hopefully there's a bit of re-investment in the area in the coming months.
If you are in Yellowstone in June, access to bathing in a thermal feature, the Boiling River, just N of Gardner, is not to be missed. It's just at the 38th parallel as I recall. Last time our path was temporarily blocked by a gang/club of massive elk bulls.
Len that picture is absolutely breathtaking. My wife loves waterfalls, we just got back from Zion, Canyonlands and Arches national parks, and I showed her your picture. She just said, that’s where we’re going next!
My family has vacationed in Wyoming and Montana several times, there is much to take in. Grand Tetons, Yellowstone, Big Horn mountains are just a few of the must see places. Glacier National Park is a trip by itself in my opinion.
You should be mindful that the Sturgis Rally is usually around the first week of August, lodging fills up fast normally but it is even worse then.