What do you do with the sand from a sandbox when you move?

Sprinkle it around the yard. The rain will push it into the ground but be sure to not have thick piles, toss it around in a thin layer. Unless the yard is crazy tiny or your sand box is crazy big you can sprinkle a lot of sand and it will just disappear in the grass. Also you could post it on a web sale site like Craigslist in the free section and I am sure someone with kids may haul it away for you.