I have no problem going alone to the movies or to dinner. I do it very often, mostly because I hate waiting for people to figure out what they want to do.
I don't feel weird about it because I don't go to the movies on the weekends or in the evenings when the crowds go. I want to enjoy the movie and get my money's worth (and I WILL tell somebody to be quiet!). When I go to dinner, I sit at the bar and order food. I probably would feel weird sitting at a table or booth alone. If I want to sit down at a table, I go for lunch (again, not when the groups go).
This may be off-topic, but I hate it when I'm in the mall and guys ask me why I'm by myself. It's a f-ing mall! Do I need a chaperone to buy clothes?
Hanging out at the mall stopped being a social thing when I graduated high school (AGES ago)!
OK, back to the topic... I generally like doing things by myself because I have varied tastes and I want to explore them without 'friends' whining about how it looks to others. For example, I went snowboarding because I wanted to try it. I didn't even bother to ask anyone because I knew I would've heard "black people don't do that".