I would suggest trying the Cody Lodging Company in Cody, WY. We found a place near Crandall Creek, WY, in late July 2009 for about $200 per night. It was a private cabin/house off of the Chief Joseph National Scenic Byway about 15 miles from Cooke City, MT - the NE entrance to Yellowstone. The North Fork of the Clark River follows the Chief Joseph Byway from Cooke City southward. Also near Cooke City, the Beartooth National Scenic Byway was about 10 miles from the cabin. Definitely the later in summer, the better. In mid July, most of the streams were still very fast. The Cody Lodging Company's website can be found online. We did stay in Dubois for a night on the Wind River, but the scenery is still mostly high plains and nothing like closer to Yellowstone.
If passing thru Cody, I recommend the Cody Rodeo!! Great entertainment!!