I've got a trip to the South Rim of the Grand Canyon planned for late May. The full moon will be on May 27, so I'm looking for moonrise and moonset shooting locations without a long hike. I have not been to the Grand Canyon before.
Hopi Point, on the West rim drive, is always a good choice. I suggest you ask a Ranger at the Mather Point visitor center when you get there. Another resource would be the Grand Canyon Association. Bob Matthies Prescott, AZ
The moon will rise at an azimuth of about 121 degrees that night -- well south of straight east. Therefore you might find that locations along the North Rim will give a better opportunity to catch the moonrise across the canyon, rather than through the trees. Along the South Rim, there might be a few overlooks along the East Rim Drive that jut out into the canyon enough to catch the moonrise along the edge of the South Rim, but it will be tight. Shoshone Point looks like the best bet. On the North Rim, Cape royal would be the natural spot, although other overlooks, such as Point Imperial might be good.
I've found that the Photographer's Ephemeris software make identifying and visualizing the locations of the sun an moon from any location very easy: http://stephentrainor.com/tools.