Plan B would be a motel in Havre. You can also camp here, but it is far from ideal:

Emporium

It's right near the railroad fuel pad, and the place was infested with mosquitoes when our group was there. We ended up getting motel rooms at the Duck Inn, which is owned by the same people.

There are also motels in East Glacier (Sears Motel there also has camping) and Whitefish. The closest campground in Whitefish is a state park a bit out of the center of town. From what I have heard, it's close to a rail yard and thus noisy.