I agree with the others May could be too early. I am a Texan who grew up going to Yellowstone because we always had to go on vacation the week of July 4th because my mother's job shut down for that week. I have played in the snow on July the 4th. My husband took me back 2 yrs a go for our 25th anniversary. We stay in Douglas in a little city park called Riverside Park, Douglas, Wy. Found it by accident has no hookup but is the cuties little park by the side of the river and you can just pull in and spend the night and it is free. They had nice restrooms with showers. For just a night's stay it was great. If you have time Douglas is a nice town to check out. If you want a beautiful drive into Yellowstone I really recommend the east enterance coming thur Cody and leaving thur the south enterance and the Grand Tetons. I think we stayed at an RV park called East Yellowstone between Cody and Yellowstone about 20 miles from the east gate was very happy with it. If you are staying in Yellowstone make your reservation early they go fast for the summer any mostly dry camping.
Texaseagle
Jim and Selena Hart