The DeMotte Campground is the nearest organized campground to the North Rim, apart from the one inside the park. I think it's 16 miles from the front gate. It's open and lovely, set in a wide meadow. Nothing fancy, nothing exciting, but facilities available which is more than you will find in the dispersed camping of the Kaibab National Forest.

Across the road is the only gas/grocery in the area. Stock up before you get there, if you head out towards the main roads it could take hours across the back roads to get back to civilization. The space is quiet and peaceful, enjoy the North Rim of the Grand Canyon while you are there.