When we moved, we went to a few local stores to ask for any extra used boxes they may have, for us to pack with. Our Kroger told us the best time to come for boxes, and let us choose from a large selection in the back. Some of the boxes also had some thick packaging paper.

A liquor store would also put out its used boxes for people to take, and some had special cardboard separators that we were able to use for fragile glass and kitchen items.