I moved to London on my own last November. Before then, I had always been surrounded by people (my family) who would come with me to things if I didn't want to be alone. I've never had many friends, yet alone friends interested in the same things I am, but I had that reassurance and if I wanted to go to a ballet, museum, movie, you name it, I could just take my sister or my mother.
This month, and also the past two or three, I've come to realize that if I want to do something, I don't need anyone with me. Yes, it's more fun and you get more out of experiences when you can share them with others, but not having a companion shouldn't stop me (or you) from doing something I enjoy.
I love movies and going to the cinema, and I bought a membership so I can go to all the movies I want, which means 99.9% of the time I'm going alone. It's a bit "blah" right after when you see people commenting but, in the end, it doesn't really matter because you've seen the movie and you've been part of the story.
Same with theatre. If no one wants to pay to go to movies, think about theatre, which is 4 times more expensive. But I do; I love theatre and don't mind paying for it if there's something I really want to see. I saw To Kill A Mockingbird just last week, got an awesome ticket (it's way easier to get a good ticket if you're just buying one), cried without feeling judged, and got to meet Robert Sean Leonard afterwards. All that happened because I didn't mind going alone.
People do look at you sometimes , but you will never see those people again. If you're afraid of doing things on your own, don't be; live the life you want, not the one others expect you to live.