Upstate SC to Grand Canyon; 4 weeks - what would you do?

On the way out to the Grand Canyon on I40 just South of Amarillo spend a couple of days camping down in the second largest canyon in the USA and check out the show that they have at Palo Duro Canyon State Park
Drive through the Petrified Forest National Park
Alternative route would be I20 to I10 then see Carlsbad Caverns with a stop and stay at Tombstone AZ on the way to the Grand Canyon
From the Grand Canyon
Would suggest Zion, Arches, Black Canyon of the Gunnison, Mesa Verde, Durango and ride the Durango Silverton Railroad.
If you like off the beaten path The Highway of Legends
IMHO trying to take in Yellowstone, Mount Rushmore is just too much to try to cram in with the Grand Canyon even in 5 weeks. That is a 4 to 5 week trip all on its own.