I'd stay in West Yellowstone and make my daily ventures from there. Tons of people in the park around July 4th so the "license plate game" is on. Flyshop row on main street is sweet...Bud Lilly's, Madison River Outfitters, Blue Ribbon etc. although their hats leave something to desire.
The quake area between Ennis and West Yellowstone on the Madison is truly spectacular so stop there. Inside the park, I like the Firehole and Lamar Rivers and Slough Creek if you are willing to hike over two or three hogbacks.
Patterns that have worked for me outside the park that time of year include small olive caddis, slightly larger olive or tan caddis with a small beadhead PT or caddis emerger as a dropper. Inside the park, keep some of the old trusted Renegades in your box sizes 14-20 plus the standard BH hare's ears/PTs/Copper Johns and so on.
If you want to experience the fray, drive up to Buffalo Ford below the lake and hit an epic BWO hatch for Yellowstone Cutties...if you don't get run over by a bison or a fat housewife you'll be golden.
