On my way down to Yellowstone, I spent one evening and the next morning hiking and photographing Hyalite Creek in the Gallatin NF outside of Bozeman. With a number of watefalls and cascades over a relatively short distance, the creek provides a great opportunity for motion-blur waterfall and river photography.
The trail is bike-accessible, and a decent mountain bike may well allow you to shoot all the falls in a single cloudy afternoon. Sandals are pretty key for getting good positions in the creek; my feet got soaked the first day when I left them behind. I managed to shoot apex, shower and champagne falls the first night and return in the morning for a riverside shot, arch and grotto falls. I missed alpine falls due to misreading the map and turning back down the trail too early.
Apex Falls: The river splits here, with cascades on both forks. Not sure which one is technically apex falls. The first fork (on the way down) had a great up-close vertical composition, while the falls on the second fork are a bit more removed from the trail.
Shower Falls: A pair of short cascades that join at the bottom, you can get some great waterfall-river combo shots with a wide angle lens.
Champagne Falls: Narrow waterfall set back in the canyon. It can be difficult to get a good angle, and this one gets dark early due to its location in the canyon. Definitely a good candidate for sandals.
Arch Falls: The water actually goes underneath an arch of rock here, which is pretty cool, but it's hard to frame the falls in a way that conveys this. If you scramble up to the top of the falls and wade across the creek you can get a nice shot looking down through the arch, but the sun was already over the canyon walls and creating funny light by the time I got around to trying this.
Grotto Falls: Very cool setting, but I had trouble framing it well. The river bends right after the falls, and you really want to be river left to compose the shot, but a steep wooded hillside makes this difficult. I got a good angle by scrambling up to the top of the falls and shooting down through trees.
Riverside: There are a couple good places to get river shots on the way up the trail. I had real good luck with one near the bottom, but it's location is difficult to describe. As you're hiking up from the parking lot, stay right at every trail junction. Eventually when the trail gets close to the creek you'll see a use trail leading off to it with a good vantage point.