Since you have already experienced the South Rim, my recommendation would be to go to the North Rim. It's a different experience that in some ways is better than the South Rim. The views are much more expansive due to the higher elevation. From the area of the North Rim Lodge, we were able to see the San Francisco Peaks near Flagstaff. From Point Imperial, we could see Navaho Mountain north of Page. The views of the canyon itself are better at the South Rim, but nothing beyond the far side is visible.
The North Rim is also close to Zion and Bryce Canyon, which are spectacular.
In addition to the National Park campground at the North Rim, There is the DeMotte Forest Service campground not far from the entrance station and another Forest Service campground at Jacob Lake. If you need hookups, there is Kaibab Camper Village at Jacob Lake.
We have been to both the North and South Rims twice and plan to go back to the North Rim again next year.