Sometimes getting a permit into the Grand Canyon is impossible. I have applied and been turned down. But don't be discouraged. There are some awesome trails and campsites in the Kaibab National Forest. Crazy Jug is probably the most famous but if you have all wheel drive or an off road Bike, you can get almost any where in the forest for a great adventure.
make sure you have a road map. There are hundreds of back roads that act as a maze so don't get lost :)