Have you been to the Grand Canyon?
It sounds like the South Rim would be more of a diversion from your route, and I'd avoid it during the busy summer season. But the North Rim may not be as far, and is certainly not nearly as busy. There are very limited lodging options at the North Rim, but you may luck out and find an opening. Or stay in Page, and see Lake Powell also.
Since I'm in AZ, I just had to put in a plug for our state somehow....