Lotsa good fishing in the North Fork Shoshone, at least if it calms down by the time you'll be there... the past few weeks the river's been so high and fast from snowmelt that 2 of our campgrounds have sites closed due to flooding (Wapiti and Big Game). Hopefully it'll be better by the time you're in the area.
If you're not camping in a hard sided vehicle or trailer, you can still stay in Rex Hale, Clearwater, Wapiti, Elk Fork, or Big Game campgounds, although I wouldn't recommend Rex Hale in a tent, as there's very little shade and way too much wind. All the campgrounds farther up the river toward Yellowstone are hard-sided only due to grizzlies (although grizzlies have shown up in every campground on the corridor). Sites can be reserved at all those campgrounds except Elk Fork, plus they all have first-come, first-served sites as well. If you want a site on the river, all those except Elk Fork have some, but Big Game and Wapiti are a bit sketchy right now with the flooding.