drook@drookenstein:/$ cd / ; sudo du . | sort -n | tail\n442212 ./home/drook\n442220 ./home\n1138716 ./usr/lib\n1141132 ./usr/share\n2819856 ./usr\n3512344 ./var/cache/apt/archives\n3525888 ./var/cache/apt\n3539036 ./var/cache\n3908908 ./var\n7856917 .
So it looks like /var would be a good candidate. Now to go look up those directions I followed for moving /home ...