I do most things by myself and these days I don't really have a big problem with it in terms of being self conscious. I live by myself in my own house, I go to movies at the cinema by myself, eat at restaurants and go to bars by myself, go to concerts and music festivals by myself. I don't have any particular problem going out with other people beyond my regular social anxieties, but there are positives to going out solo too. Don't have to split up the schedule or make compromises or talk over plans, you can just do what you want to do.
I am almost 28 now and this confidence to be able to go out by myself is the result of me forcing myself to do more to get out of the house all day until it no longer bothered me that many do prefer going with others to these things.