We've stayed at Point of Rocks and the top level was pleasant. It's a smallish park.
Would Williams be too far for you? The parks there are family-tourist oriented.
How about Elk Pines in Heber? Show Low Lake Campground? Ponderosa RV Resort, Pinetop? HonDah Casino, Pinetop?
http://www.rvparkreviews.com/regions/arizona/heber-overgaardGood luck!