If you decide to try the North Rim, you might want to keep heading north on US89 to Page, AZ first. The Glen Canyon Dam and Lake Powell rec area is there, if you like that sort of thing. It's about 2.5 hours from Mather CG one way.
On the same (dam) theme, in the opposite direction, along I-40 towards Kingman, AZ then north on US93 to the Hoover Dam. It's a bit of a drive from GC, about 4 hours, so you could stop there before you head to Grand Canyon Village/Mather CG on your way out from Socal, if you have time for a side trip.
