We've stopped at rest stops on occasion but they're sure noisy with all the trucks. Some rest stops don't allow overnighters but we've never had a problem.
We used the boondocking app, last summer. We spent 3 nights, a few miles from Tusayan ( at south entrance to the park). We were 3 miles down a National Forest road FS 302), by ourselves, pretty country and managed to see a small group of elk one morning. memtb