The Middle Fork of the Flathead River runs out of the Bob Marshall [1] and Great Bear Wilderness Areas [2] and along the southwest border of the park to West Glacier.
Along the edge of the park, the tiny town of Essex is home to a classic old hotel, The Izaak Walton Inn [3].
Links:
[1] http://www.moon.com/destinations/montana/missoula-and-northwestern-montana/the-swan-and-blackfoot-valleys/bob-marshall-wilderness-area
[2] http://www.moon.com/destinations/montana/missoula-and-northwestern-montana/north-flathead-lake/hungry-horse/great-bear-wilderness-area
[3] http://www.moon.com/destinations/montana/glacier-national-park/west-glacier-and-the-flathead-river-middle-fork/accommodations/over-100