can't go wrong with yellowstone
Yellowstone, being the beautiful place that it is, is one of the most well trafficked national parks in the U.S. This being said, it's campgrounds fill up super quickly. If you're looking to stay within the park, plan your trip pretty far in advance so you can be sure to get a spot. However, there are some campground that don't take reservations and just do it one a first come, first served basis.
Norris campground is one that does not take reservations. When my friends and I were coming through Yellowstone, I thought it was super lucky that we managed to find a site. The sites are pretty nice too; flat and some are pretty secluded. They seemed to have a lot more tent sites than RV sites, so if you have an RV, I wouldn't necessarily bet on finding a site here.
Although the camp is nice, you don't spend much time at it when you're in Yellowstone. The park is beautiful. I prefer the less touristy hikes, but of course you have to go see Old Faithful and The Grand Prismatic Spring and all the other touristy things.
Get out there and have fun!