Well, you have major two choices right off the bat, North Rim and South Rim.
The South Rim is the more famous of the two and what most people typically consider "The Grand Canyon." For that reason, it is more developed and, thus, more crowded. Despite that development, there's only one choice close to the rim, which is the Trailer Village RV Park. If you can get in, it's a great place to stay as it is within walking distance of all of the South Rim "attractions." We stayed here last halloween and loved it . . . Otherwise, there are some parks outside the park entrance.
North Rim is more remote and, for that reason, less developed and less crowded, but just as beautiful (ANYWHERE along the Grand Canyon, South Rim, North Rim and everywhere in between is spectacular). There are a number of RV parks around the North Rim, but they are seasonal.
Make sure you take a day to hike down into the canyon itself - well worth it (not down to the river and back, but just down far enough to really appreciate this natural wonder . . .)