On my last cross-country trip I stayed in a few parking lots. The only trouble I had was the very first night when I pulled into a rest stop. I found a parking spot and had got out of my seat and was walking to the back when there was a knock at the door. It was several obvious transients who wanted a ride. They were a little demanding, but went away when I made it clear I was not giving them a ride. So we pulled out of there and went down to the next town and stayed in a Walmart parking lot.
If you do a Google search on rest stop crime you'll see some rest stops tend to attract some unsavory characters.
