Welcome to the Carolinas, in advance!
Hello Unlikely,
By all means I second Southwest Dave's recommendation to exit Grand Canyon National Park from the East Entrance and follow AZ 64 to US 89 and thence back to Flagstaff and I-40. There are some views of the upstream tributary canyons, viewed from the highway between the East Entrance and Cameron, AZ, which are quite memorable.
There is a loop thorugh a volcanic cinder cone area just to the east of US 89 a fairly short distance north of Flagstaff which is probably worth a look, too.
I am of course biased in expressing curiosity as how you chose "the other Carolina", but I welcome you nevertheless!
Foy