Yellowstone Late May to Mid June

Well, I would suggest that you go ahead, just be aware that it could snow and be a little cool in the evenings. At the very least come in from the south entrance, after going through Grand Teton National Park, and then have a good time. Lodging might be a problem, but with advance planning you should be ok. Be flexible, if a road you want to travel is not open, others will be. If you get up to the north part of the Park, things should be good for you as that end of the Park is open year-round for highway travel. On the way through Grand Teton you will have a great chance to see wildlife, especially early in the morning and in the evening. As well, you will probably see wildlife on the way from Grand Teton to Yellowstone as well, just keep your eyes open. Take a shot and have a great time.