Lurker,
In the last 14 seasons of RiVing, we have done all that stuff. Walmarts are real convenient, so are lots of other places. There are good web resources that can help you find them. At any business concern, always ask. At many, we go in (Walmarts particularly) and ask a manager if we can stay overnight when we get done shopping.
We have slept over our APU more that a few times both for heat and because of.
If you can bear the noise, just have at least one good CO monitor going. Waking up dead is real easy to do.
Matt