Here's the official Yellowstone campground site:
Yellowstone CampgroundsIf you're already in the park you might consider checking at your reserved campground the day before you leave and again in the morning. Many times there are cancellations and you could then just stay where you are.
We love Mammoth and our 40' MH fits just fine. The views along the ridge are gorgeous and you'll usually have elk walking down the street. This is a handy campground if you want to explore more of the north area and for even taking a day tour north.
We've also pulled into Madison and Bridge Bay early morning and easily secured a site without reservations. Give it a try and have a good trip!