Thanks for the feedback.  I should have mentioned I'm interested in the "moving water" part of the river that's north and east of the park, not the Class III stuff near Gardiner.

I also realize that I-90 runs parallel to the river for the most part.  That is the unappealing part of my thoughts.  However, such an expansive valley and neat moving water sounds so cool, not to mention it's the Yellowstone.

The Upper Missouri sounds interesting, too.  I'll have to look into that.