I did GC early July last year. For free rim camping Timp Point north to Parrisawampitts Point has campsites most points from memory. Further north Crazy Jug Point to Bill Hall(FR292A) has some pull outs off the road for dispersed camping. To camp right on the rim in the national park(Point Sublime, Swamp Point, Fire point, ) you need a backcountry permit($18) from the backcountry office near the North Rim Visitors centre. For me the national park campsites had much better views than the national forest spots.
Also FR250 was an awesome drive going through pine forests to aspen groves with old homesteads hidden in the forest. I did it in the rain and it was easy.
I did a write up for
my try here if you want to see photos of a few places I camped on the north rim.