Going out to eat or to a movie alone was one of the most difficult things to get used to after my divorce. I felt so alone and like such a loser and felt that people were judging me. A big part of that was likely due to how raw a person can feel after a divorce, and also having to get used to things being different.
I don't see how going to a movie alone would mean anything. People are there to see the large screen.
Nevertheless, I have a set of rules I tend to follow when I go to the cinema (a practice which has faded out of my life). I would go in the afternoon showings, 1 - 4pm, avoid Matinee crowds, avoid going on Friday and Saturday nights, and if you can reserve a seat, make sure you get one where it's centered so you get the maximum viewing experience. Also, visit a cinema when the movie is about to be taken off the cinema. By this time the hype of the movie has died down and you may only get one or two souls inside the same cinema or even get an empty cinema to which to enjoy the movie all by yourself!
I do not have a set of rules for eating solo since I don't actually do that. I would imagine I'd probably bring a tablet or portable device with some head-phones if the environment bothered me, so at least my mind could be distracted by something else so as not to really care about that if I'm there for an extended period of time beyond eating the meal. Or, at the very least, as a Christian believer, knowing Jesus is present inside of me so I don't care what other people think about me as long as I'm right with God. If I feel lonely then it's because my prayer life is neglected and it's my fault.