Try to spend some time in Waterton NP and Glacier NP in Montana. They are both beautiful, although it will be a shitshow at this time. Hit up The Park Cafe at the St. Mary entrance to Glacier NP. The Going to the Sun Hwy is a great drive. I'd say do it at the crack of dawn when traffic is light. I don't know anything about the 12 but the I-90 is a good way to kill a lot of miles westbound from Missoula. The speed limit is 75 mph most of the time. Coeur d'Alene is nice. West of Spokane, the I-90 becomes the most boring drive on earth but it's good if you want to get somewhere fast. When you hit Hood River, go South to Mt. Hood and get the 97 South through Bend, Smith Rock State Park, Deschutes Nat'l Forest etc. on your way to Crater Lake. There is a lot to see and do in Montana and Oregon.
I apologize for this ^ miserable paragraph. Have fun!
LISTEN TO THIS MAN. YMMV but Going-to the sun road probably won't be open all the way. I was there June 30th and it was surprisingly not crazy busy, in either Waterton or Glacier.
_MG_6308.jpg by crashmtb, on Flickr
anyway, Sleeping without a tent or some other form of physical barrier between you and various biting insects is foolhardy, even though the mosquitos around there are tiny and amateurish. Your delicate island skin will prove no match for the copious mosquitos. I found them tiny and slow. But I'm from Manitoba. :D