"Buster52".....The south rim is the more popular side and would typically take you at least 3-4 days to see the entire thing. There is a great campground inside the park (south rim) called Trailer Village. It has full hookups and you can board the shuttle at the entrance to the campground. Grand Canyon Village, with stores and dining, are within walking distance. The campground isn't exotic, but has all of the basics, large sites and is right in the park.
Trailer Village is booked through Xanterra. If the campground is full, which it often is, there is a private campground about a 1/2 mile from the south entrance in the town of Tusayan. It's not pretty, but it's clean, reasonable and you can walk into town at the edge of the park. It also has a Grand Canyon shuttle stop in front for the south rim. It's called Camper's Village.
Williams is a great gateway town into the south rim of the Grand Canyon. It has two KOA's and several other campgrounds, one that is especially nice is Grand Canyon Railway RV. Williams has nice antique shops and some good dining. The downside is that it's almost an hour drive into the park. The south rim of the Grand Canyon really can't be seen in a day, so there would be a lot of commuting. As I said, you should alot at LEAST 3-4 days of sightseeing.
Most of the park can be seen by using the shuttle system. It will take you around the majority of the south rim, but there is another attraction, Devil's Tower that is east of the south rim about, 20 miles, that has several stops on the way. You'll need a car for this....worth seeing.