I strongly recommend the south rim of the Grand Canyon - it's the view that will take your breath away at first sight. North rim, not so much.
Plus, you can boondock just outside the main entrance at the south rim. It's quite surprising but there is a national forest site about one mile or less (on the left) as one approaches the south rim National Park entrance.
I only stayed one night at the boondock site - the ground is very powdery and tended to feel "dirty" when I was there. I didn't like it, but it was a place to stay almost within the park.