As for the "doing things alone" I've noticed that people don't like doing that. Traveling, going to see a movie, or attending an event all seem to be things that have a stigma attached to doing them solo.
Example #5 Going to a park, especially an "improved" park with kids playground and you're a dude.
Example #6 Wilderness hiking (although this is really a safety issue, and as a lifelong hiker I assure you your local hiking club is a fantastic way to meet people)
It's like Eleanor Roosevelt said (more or less: http://quoteinvestigator.com/2011/03/30/not-inferior/): "No one can make you feel inferior without your consent."
Not doing something you want to do because "they'll all laugh at me" is you giving your consent to being made to feel inferior. Their opinion only matters because you make it matter, by caring about it enough to let it stop you from doing something you want to do.
You may feel like their opinion puts shackles around your ankles, but really the shackles only exist in your mind. Stop believing in them and they disappear.
I disagree. If enough people in your community say that you are unwanted, you will become unwanted.
I remember my conversation with the hostess going something like this:
Hostess: "So...just one today?"
Me: "Yep."
Hostess: "Oh.. Do you want me to bring you a magazine or something?"