Nick, Watchman and South are the campgrounds right in the park. Watchman allows you to reserve certain sites (mostly along the river, I think). South campground is first come, first served. South is more heavily shaded and cooler in the warm weather. That's the one we preferred. In the busy season, I understand you have to be in line first thing in the morning to get a site. Also, there are no hookups so it will be hot in the summer, but the nights might be bearable.
If you are coming from the east, you must go through a tunnel. With an tall trailer, you pay an extra fee. Our Casita
at 8.5 feet high was below the limit so no fee.