Well, I'm not so sure about this. If I saw someone sitting alone at a restaurant, or going to a movie alone, I wouldn't give it a second thought. I do those things alone, because the only other person I know is my husband, and one of us needs to stay home with the kids. Also, I enjoy my own company.
First a disclaimer: I've come to the conclusion that, although I have a few AS traits, and I'm definitely an introvert, and haven't the foggiest clue how to get to know someone, I'm not actually on the spectrum. At the most I'm borderline AS.
Anyway, I go to public places alone. I always have. I go to movies and restaurants alone, and certainly go shopping by myself. Why wouldn't I? And how is that creepy? If people do find it creepy, I suspect that would have something to do with their own insecurities.
In fact, next month I'm flying to New York and attending a play all by myself. I don't know anyone who can accompany me, but I'm certainly not letting that stop me, because the play stars Alan Rickman. My desire to see him on stage is far greater than any fear of doing something alone (and this is way out of my comfort zone). No one is going to notice or care about me being there alone. They'll be watching the play. If they get creeped out by my aloneness, then they certainly need to reexamine their priorities.