I'm pretty sure you are talking about the South Rim which is where most people visit the Grand Canyon, but I will mention anyway that we just stayed at the Kaibab Camper Village RV Park in Jacobs Lake, AZ from where we visited the North Rim.
http://dwilliamson.com/GrandCanyon/Page.html
It was a very nice forested campground. If you ever have opportunity, you should visit the North Rim which, in my opinion, is the best way to view the Grand Canyon -- and away from most of the crowds.