Many Wal-Marts welcome overnight "guests" to stay in their parking lots with campers or RVs. In fact, I think the ones that don't allow it are mainly (all?) those wherein the municipality does not allow them to welcome campers.
Campers are grateful for this, and as such try to leave a light
footprint (or should anyway, IMO). So, no setting up tables and chairs, try not to use slide outs, no grilling, park way out at the edge, etc. Also, it's courteous to do some shopping if you need to (admittedly I don't typically do this when I'm camping there, but I do shop at Wal-Mart on a regular basis; also I do not go in to use the bathrooms if I'm not shopping).
I would be a bit uncomfortable about leaving a rig there overnight unattended. Not so much in worry over the rig (depending on area of course), but more because Wal-Mart's hospitality is so appreciated by the RV-ing world, and I would not want to do anything to jeopardize that. I'm not sure that leaving a rig there for storage might not do that. (Granted, physically it is no different than if you were in the rig, but still - maybe they would need you to move it, or what if someone stole it or broke in and then they found out you weren't there - or were worried that you had been absconded with or etc.)
But I empathize: Isn't it a pain how many areas do not allow RV parking? Say, one thing to check: Some places that do not allow RV parking will allow it for less than 24 hours.