Best way to move docker directory
Ubuntu:

docker ps -q | xargs docker kill

service docker stop

cd /var/lib/docker/devicemapper/mnt
umount ./*

mv /var/lib/docker $dest

ln -s $dest /var/lib/docker

in /etc/default/docker: add: DOCKER_OPTS="-g $(readlink -f /var/lib/docker)"

service docker start