Yellowstone Lake, or for that matter any of the high, cold lakes, will be OK then. End of June is better (water temps are still in mid-to-high 40s within about 20 ft of surface), but depending on runoff the streams can take until July to clear. If runoff is heavy, end of July will be great as streamwater temps won't be dangerously high.

I believe the Yellowstone opens on July 15th inside the park (in Hayden Valley anyway) and can be excellent.

The Madison should be fishing well, as should the lakes along its drainage (Hebgen, Quake). The Firehole gets a tad too warm by that time of year usually, but the Gibbon can also fish well. I'd recommed trying the Gibbon, in fact, as you might luck out and get into a grayling or two!

Marty