I'm jealous! I'd love to fish in West Yellowstone on opening weekend.
I love the Firehole River. It's amazing! If you go to Fountain Flats parking lot, it takes you to a nice stretch of the river where you can get away from the crowds. Opening weekend can get very crowded.
Check out this blog: Fly Fishing In Yellowstone National Park
It will give you very pertinent info. about opening weekend for fishing in YNP.