If you can live without hookups: In a less developed area, the NPS Desert View Campground, at the east entrance to the park (25 miles/ 41km to the east of Grand Canyon Village,) is first-come, first-served only.
No reservations are accepted. There are no RV hook-ups at Desert View.
http://www.nps.gov/grca/planyourvisit/cg-sr.htm#CP_JUMP_153567This is in high, dry Arizona, you should not need electricity for the A/C. It will be cool up there....even if warm in the daytime.
We have used the Forest Service Campground near Flagstaff & Sunset Crater Nat'l Mon'l to do a day trip to the canyon in the past. Also first come/first served & no hookups.
Bonito CampgroundOther Forest Service
Campgrounds.
Dispersed CampingGrand Canyon Trailer Village might have a spot by the time you get there as well. ? Not all reservations are kept.
There are several RV Parks in Williams:
RV Park Reviews