We just came back from the GC South Rim. If you are coming through in May go to their site and reserve a campsite in Mathers Campground (inside the GC) now because they fill quickly. They have hot coin showers and a laundromat in park next to the campground. I highly recommend getting the adventure pass for the National Parks. It's about $80 annually but it pays for itself after two trips. You get into the national parks for free and you get discounted camping 1/2 price and discounts at the gift shops too. We paid $16 for our entire 3 night stay over President's weekend. They have a fun Jr. Ranger program for kids to earn badges. After you leave the GC as you continue down the 66 stop at the Petrified Forest, another NP along the route and so cool. The spaces are very big. They do not use artificial light at night so bring flashlights it does get very dark.
http://www.nps.gov/grca/planyourvisit/cg-sr.htmWhen you hit Needles follow route 66 through Oatman. the road is smaller but the wild burros are in Oatman and a fun stop. We saw bighorn on the road after we left Oatman. It's about a 10 hour drive with a trailer from Mojave CA to the South rim on route 66. It's very crowded on the South Rim in the summer, they bus people in to cut down on traffic. Bring water, food, and firewood, these are all expensive at the store in the park. We had a huge herd of elk stay with us in the campground when we were there and deer every morning. Secure your food and belongings the ravens will get into them faster than you can walk back to camp. We watched them defeat all kinds of zippers and bags, use plastic tubs in other camps. Poor folks came back to food and clothes everywhere.
We are staying at the North rim in July so I'll post photos when we get back.
Message me and I can also share the great food stops along the way. In Albuquerque there is a KOA off the freeway.