I know that Knoll Lake up on the Mogollon Rim has large spaces, because it's just the woods. We were up there this weekend and were next to an ENORMOUS group of Boy Scouts, but were still far enough away (we'll not far enough for the lady who dropped her pants to pee and flashed her ass to us I guess) that we could only hear them, not see them. Also, there is no fee for Knoll but you need to get there early to ensure larger areas. As for amenities, I find that those campgrounds are filled with people and campsites are right on top of each other so people get mad if you are loud. I don't know much about the Flagstaff area so I'm no help there, but if we had a better idea of how many people are interested and what kind of set ups they will have might make it a little easier to determine how much space we would need.