What route are you considering……. big picture? Which boils down to which way are you going around the Grand Canyon? East side (Page or Jacobs Lake/Lees Ferry to Flagstaff or west side, St. George to Vegas? If the former how do you plan to get to Fredonia or Page? Both the USFS and the BLM have online info on numerous camping possibilities as well as “at large” camping but here’s probably so much info you might need to hone in on a route. On the East side of the Colorado there are at large sites and some developed sites all round the Needles, Abajo Mts., Bears Ears, Cedar Mesa area. On the west side of the river there are sure to be about a bazillion possibilities in Fishlakes and Dixie National Forests. As a maybe wayout example Google Crazy Jug Point on google maps and look at that little circle drive on the point. I camped there once and it is spectacular! Hopefully the kids are old enough to understand not to walk over the edge! That’s accessible by a “normal” sedan.
What is the comfort level of your group? Can they get by without “facilities”. That could be an Occam’s razor of a sort. Taking the kids (and dog) can create a whole new set of responsibilities. You probably ought to consider facilities at least most nights, or have some pretty good facsimiles available. The forest service probably has the most developed sites with facilities but States Parks are often pretty good ; for example the Coral Pink Sand Dunes outside Kanab has hot water showers! And lately even the BLM has been adding a few more developed facilities.
So pick a facility level that’ll keep the group reasonably satisfied and morale high. You just about can’t miss on scenery.
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