We just bought a box bike (from the Dutch "bakfiets") from Urkai. It's quite a bike. It's large, long, heavy. But it rides smooth and easy even when the box is loaded with a kid and everything for an outing.
It's been pretty fun. We immediately took the bike to an nearby town for ice cream (we have priorities). It was over an hour each way along a gentle rail trail. Our toddler loved it. On the way back it was getting dark so the built-in lights came in quite handy. And we could flip up the bench so our kid could sleep in the bottom on a pad.
We've wanted a Dutch-style box bike for a while. We've already got other Dutch bikes and appreciate the low-maintenance and comfort. The Bakfiets.nl cargo bike with electric-assist that we got is really well-built. The bike came in two boxes; one really long narrow box that held the frame and wheels, and the other held the box. Urkai is based in Burlington, Ontario, but ships anywhere in Canada.
Full disclosure: I approached Urkai about getting a discount if I wrote up my experiences, and owner Andrew agreed.