I stayed at the 1st motel on the left (across the street from the buffalo burger stand) as you ride
into Red Lodge after going over Beartooth they had a pool too !
You will not get to ride Highway to the SUn in Glacier in June IMHO wont be open for season yet
but check with Natl Park Service website
Its a nice day ride from Spearfish to Cody lots to see there
How far west you want to go Lolo Pass is really nice if you are going to Missoula thats where it Starts
Probably wont be snowing too bad there if it snows at all
remember when you get to the ocean you have to go north or south

unless you are doing a Gump, head back same way