Hello Photoman Phil:
As mentioned above, the simplest answer is it is illegal to pilot your drone within the boundaries of a National Park in the United States. There is some debate about whether or not you can legally fly your drone into a National Park from a piloting position outside of the boundaries. If your review of regulations in the United States convinces you that you can fly over the National Park boundaries from an outside piloting position, then you might find sections of the Grand Canyon’s North Rim west of Highway 67 useful. If you’re driving a high clearance vehicle there are Forest Service dirt roads that run west and reach sections of the North Rim administered by the US Forest Service. Within Forest Service lands you can fly your drone. In some of those areas, the boundary for the National Park is the actual edge of the rim - into the canyon is National Park, outside of the canyon is National Forest.
Even if you were not convinced that launching in the National Forest and flying over the National Park was legal, there are areas where you could launch your drone, fly up less than 400 feet, and rotate your drone for spectacular views of the Grand Canyon. Admittedly this would take extra time and a capable vehicle to reach those regions, but my wife and I find those regions more enjoyable than the more crowded areas of the North Rim within the National Park.
Have a great trip!
Howard