i cant stress this enough.. what do people say when they a) want to get out of the heat or b) want to go camping?
"im going up north"
thats right, pro'lly 95% of Mem. Day campers do this only 1-2 times a year, and the only place they think you can camp (or that offers cool weather) is the Mogollon Rim. Try it.. ask your people where they like to camp. I have a high degree of confidence they will say "im going up to the Rim"
You can safely bet that there will be about 14,395 camps set up on that section running from Happy Jack to Woods Canyon. Want to go to the Rim but avoid crowds? Do it either on some random weekend or go to a place like the top of West Clear creek and use the Calloway trail to get down to the water, if you desire.
In light of that, how many people do you hear say "im going down south"?
so im sticking with my previous advice: go south
but if you still want north
but desire thin crowds? go where people cannot take their monstrosity house on wheels and do some primitive camping in a "locals only" type environ. I'll even give you this one: Howard Pocket. Take the 89a out of Sedona about a mile past the switchbacks and turn onto the only left leading away from the hiway, fr535. Drive 535 to the signed 536a turn left and take the road to the edge of West Fork canyon to get spectacular south-facing veiws of W. Fork, and all of the Red Rock valley below. There will be others there, no doubt.. but the road 536a weeds out two types of people: those that drive Honda Accords and those that drive toy haulers. (and fwiw, its still officially "the rim"