One way to avoid the Yellowstone crowd is to go Grand Teton park. It boarders the south side of Yellowstone. It's easy to camp in Tetons and drive to Yellowstone as a day trip. The Tetons have great mountain scenery. Campgrounds in the two parks are run by the National Park Service. Check their website for current rules/rates. Have tent camped there several times and found it very clean and safe. I noticed you said "late spring." Earliest I went was in early June. The higher elevation road between Tetons and Yellowstone was recently opened with snow on each side. Jacket weather during the day and quite cool at night. The National Park Service websites are packed with good info. Can't say enough good things about the rangers at those parks. Enjoy.