Search for North Fork of the Flathead (west border of Glacier NP) and the Blackfoot River (parallel to US200 between Missoula and Ovando).
Both have good camping opportunities, scenery, fishing, and Class II's.
NF Flathead is NPS land on river left, so you need a backcountry permit (inconvenient to difficult to get) to camp there. River right is intermixed private and Flathead NF land. There are NF accesses every 15-18 miles. More difficult access/shuttle up 50+ miles of gravel, but incredible views up north.
Blackfoot is mostly private land on both banks, but there are state fishing accesses and a few campgrounds at decent intervals. Easier access. Pretty nice scenery--kind of a "ranch float" past cows and hayfields for a lot of parts.