Unless it dumps rain, you could do all of the wade fishing in that time frame within WALKING distance of Gardiner, and there's a million places to fish within an hour drive, both inside and outside the park.

Expect Salmonflies to still be present in the Black/Grand Canyons of the Yellowstone and maybe the Gardner, plus Green Drakes in the Lamar system. All rivers in the northern part of the park should be at basically their most consistent in mid-July this year. It'll be a couple weeks after runoff basically drops out, so long enough for the hatches to become established, but not long enough for the fish to be spooky yet. Roadside and famous rivers (and especially famous rivers right next to the road) will be crowded, but there's a lot of water to spread out in.

I don't know if you're the guy who called me earlier this week who was planning for late May originally, but this is a MUCH better timeframe in terms of options. My clients often don't fish anything but dries then, and there's really no reason to expect to fish deeper than dry-dropper unless you want to strip streamers.

Also, "blue ribbon" and similar distinctions are wildly overrated. I'd rather fish the Gardner over the Madison any day the former is clear enough. The fish aren't as big, but neither are the crowds. There are lots of famous rivers around here, but the creeks are at least as big an attraction for me.