In addition to the Grand Canyon, you might want to stop at Monument Valley. It has its own strip, dirt when I was there but now blacktop I believe. It is an extraordinary place and absolutely worth visiting. It's a 10 minute walk from the strip to the hotel, or they'll pick you up. You need to get permission before going there but it's straightforward.
For the Canyon, for the non-airplane visit, the North Rim is much more spectacular than the South Rim. Unfortunately there's no strip anywhere close, the nearest place with car rental is Page which is about a 2-3 hour drive - but the drive is also spectacular, especially the return when the Vermillion Cliffs have been switched on.
I did "fly the canyon" once but there was so much smoke from forest fires that the view was not especially spectacular. One thing I'd recommend, once you've got the SFAR chart, is to enter the entrance and exit points of the corridors in the GPS (for some reason they don't have VPxxx names). That way you can put them in a flight plan and be sure you won't fly where you shouldn't.
Enjoy...
n5296s