I can reccomend the following: Go to Williams. There is a campground or two there...and sign up for "The Train".
In fact, google "The Train"...south rim. They have a hotel, (park your RV in the hotel parking lot if you choose to stay in their hotel) 2 hour train ride (Very entertaining) up and back. 1 day, 2 days 3 days, etc....some meals included, a wild west show and well worth the price. (we signed up for 1 nite IN the canyon. Yavapi (sic) Lodge)
The "in the canyon" hotels are run by another company and the hardest part is scheduling both at the same time. Via phone.
We had dinner at the "Arizona Room" in the south rim...I have no idea if it is still there...but if it is, prepare for a treat. I don't know if it was the altitude, the pre-dinner drinks (had to wait an hour or so for a table), the good company, or a combination of all three...but it was the most memorable steak dinner we've ever had.
If you do this, bring a wad of 1 dollar bills. Everyone works on tips. Especailly the outlaws that hold up the train on the way back.