I agree with Yonan, the North Rim is a spectacular place to visit. I've stayed on a couple occasions in the national forest right along the rim. I take the last forest road to the east (611 on Google maps) just before the park entrance. If you get to the entrance grab a park map and talk with the rangers. Then make a U-turn and take you first right into the forest. Just wander back through the woods and you'll find sites all along the rim.
A couple of years ago I had good luck showing up at the North Rim campground early in the day and waiting for cancellations I was able to stay three nights without having a reservation.
There is some off-road camping within the park. Point Sublime is one of the most spectacular 300 degree views of the canyon. It's about 20 miles off the main road and didn't really have any challenges. If you want to spend the night there you'll need to make a reservation ahead of time since sites are extremely limited.
Another spectacular stop before the North Rim would be Toroweap on the west end of the Grand Canyon. It's 60 miles off Hwy 389 and is an easy off-road, although the last mile has some bumps. Again, reservations are recommended. I was able to get two nights by checking with the rangers at Pipe Spring National Monument (on Hwy 389 before the Toroweap turnoff). They called the North Rim ranger station and got permission.
Have a great trip.