Yellowstone is completely awesome in August. If you can swing it, hit the park the day after Labor Day. Weather is still nice, most of the park facilities are still open for another week or two, wildlife is moving around (getting ready for winter), and most of the tourists have cleared out.
If you are into fly-fishing, this is when you want to go. Hardly anyone will be fishing, and all the streams (where you are allowed to fish) will be open. Did you know the Yellowstone River inside the park does not open to fishing until July 15th (to allow the native cutthroat trout to spawn in peace).
I was there Labor Day weekend 2002, and spent 2 hours walking/hiking the 5 miles back into the 1st meadow on Slough Creek. This is a world famous location for fly-fishing. Couldn't believe that I had the entire meadow to myself (unheard of). Caught and released around 30 cutthroat trout that day. Had to wait for a moose to get out of the way (was standing on the trail) on the way back to the car.
Ended up driving over to Cooke City that evening. Found an old hotel/restaurant/bar, around 10 at night. No one else there, so I ended up eating a spaghetti dinner and talking with the waitress (actually helped her clean up/vaccuum the place). She gave me the phone number of a hotel to crash out at that night (only $25/cash). Ended up spending the night, until about 3 in the morning, talking about fly-fishing with the hotel owner. We actually tied about a dozen or so flies that night while trading fishing stories.
The next morning, I headed back to Denver, Colorado (where I was living at the time). Actually, ended up using the experience as the basis for my undergraduate nursing school admission thesis (it's somewhere here on allnurses.com ... can find by doing a search).
Anyhow, it's something to think about.
I graduate (hopefully) in Dec 2018 from Univ of Pgh - DNP/PMHNP program. I am actually planning on driving down to Disney World about 10 minutes post graduation. Not sure if I will go to the parks or just lie around in the hotel for an entire week. I'm already 3 years into the program am so utterly ready to get it over with.
Whatever you do ... have lots of fun. :)