One day for GC a bit tight. You mean 1 night? Like that can but you will really be driving for a very long time if it is the South Rim you are going. Got buddy driver or not?
Before the plan I had, I nearly wanted to go South Rim then go to Flagstaff, AZ for the Lowell Observatory. In the end was way too long. Since North Rim less people go, I took North Rim but base must be in Kanab, UT.
Since got 1 night to slot in, see what sights you can see along the way. I assume you are driving from South Rim to Anaheim, CA? Then check out the old Route 66! That was my original plan. Visit the ghost town of Oatman, AZ. I think there are sections of the road that are marked with the Route 66 symbol. Drive on it and make sure take picture of it. Seligman, AZ is the place were you can go to
Delgadillo's Sno Cap Drive-In. That stop ice cream place/diner is the inspiration for Pixar's Cars. The other place to go here is the Roadkill Cafe.
There are lots of other stuff along the old Route 66 since you are going down to the South Rim. Williams, AZ is also another stop along the old Route 66. It is also the site of the Grand Canyon Railway.
http://www.experiencewilliams.com/
If you are going to drive from South Rim to CA, might as well visit these towns nearer to the South Rim, then stay the night on any place along the I40 on the way the CA.