Seattle to Butte Yellowstone Rapid City Medora.Best Route?

Yellowstone National Park is open year round. Most, if not all, of the park's campgrounds don't open until May. Check the parks web site for the right information. Most likely what you will encounter in the park in April is snow, snow, snow. Even if you stay in West Yellowstone you might not be able to get into the park from there due to weather, spelled snow. Friends of ours went in early May. Fishing Bridge camp sites had been plowed, but not the area between them so snow was piled real high.