The Box Canyon of the North Fork Teton River is a very nice class II-III whitewater run through a dramatic but open limestone canyon. The road access, relative rarity of strainers, ease of scouting, and moderate bedrock and boulder whitewater make this a good option for intermediate paddlers looking to experience the Rocky Mountain Front by boat.
When flows are good you will likely want to continue another 6-10 miles down the roadside run of the North Fork which cuts through numerous limestone reefs. There is great camping on pull-offs and in campgrounds along the roadside section. The South Fork Teton also offers a roadside section that is nearby.