The snake river is an amazing journey through the park. Make sure you book with a company that provides a sceninc float trip in the park, usually pushing off from Dead Man's Bar. Eagles are common on these trips and most of the time the river is gentle.
I've started shooting longer exposures at dusk of the river and this provides a great opportunity to play with motion and mountains together in one image.
Heading to the Town of Wilson while you cross over the Snake River, there are walking paths along the dikes that can give you great access to the river.
Photo by Jonathan Adams