Fly fishing outside the park can be an incredible experiance. I love to fish it all year, but in mid summer if you are in the water at day break and have some dries #22 or smaller you will have a blast. #24 griffis nat is my choice. can be a real bear to try if you not used to tying that small. After they stop rising I usually turn to a fox squirl nymph #16 OR #18.
I always wear cammo or dark close when fishing down there. if your carful and go slow you can walk up in sight fishing distance of some real monster browns. Some double digit fish and many above 5Lbs.
If fishing in the park try walking from the bridge above the campground to the end of the park, you would be suprised what most fisherman just walk by. always look at the fish's tail. if heavily forked ,not a brown but a big sucker. I have waisted a few hours fishing for Huge suckers. The browns tail will be very square or even rounded out.
Good luck, walk slow and check every rock, rootwad, and under cut bank. he's in there.