In the last few years, while gathering materials for my new book on Glacier
, I've often parked my 30-foot Classic at the Many Glacier campground. The trick is to get there early, usually about 10, but on the rare occasion I've missed a spot I return to St. Mary and get a spot at Johnson (mentioned by someone else here) or I go to the KOA. Eventually a Many Glacier spot opens up, and if you have to wait a day or so, it's worth it!
I also worked Glacier as a ranger and certainly agree that Many Glacier is one of the park's best spots at which to camp. Trails depart from the campground to Iceberg Lake, and in the other direction, to Grinnell Glacier, and the glacier's disappearance provides proof that global warming is occurring -- whatever the reason might be.
Also check out the relatively new shuttle bus routes and times, for they open up a whole new series of opportunities. Drop me a note if you want, and I'll tell you how we've used them. Good luck! Bert