I am a single woman and have traveled across the US. I have tried many different parking situations and here are some observations from my point of view (single woman alone in rig with 2 small dogs).
My only concern is safety. I love Walmart and I do check on Allstays for other peoples opinion. It has helped me make up my mind on where to stay. (bad part of town, etc). I only stay at Supercenters that are open all night, away from the store but, not isolated area and near another rig, if possible.
I call ahead to ask for permission, too. I walk dogs before I get to lot so all I have to do is park and eat and get to bed. I do not want anyone to know I am alone inside. I always shop in morning to spend money there .
I have tried truck stops but, never again. Waaay too noisy and lots "stuff" going on around. I am very careful to not get into any "lonely" situations like empty parking lots, etc. anywhere. I would try a church if there were people nearby.