Two more ideas from me: 1) Toastmasters. This is like alcoholics anonymous for people that are addicted to shyness. And very likely there will be some people there that are even more quiet and introverted than you are. 2) Social dancing. I'm guessing you are male, in which case you will be in high demand. Even if you are overweight & ugly as sin, if you can keep a beat then the girls are gonna want some. If you are a…
It seems like dancing is a super popular suggestion. I keep saying to myself that I'd be no good and it'd be embarassing, not to mention I'm not (never have been) a "dancer" but I'm thinking this swarm intellect might have a point... And perhaps I should seriously consider signing up for a beginner dance class. Any reason why Tango is where the nerds end up?
I would suggest you try whatever dance attracts you. For example, consider if you like the music. You might like swing, but I find it's too energetic & bouncy for me. Salsa always seems to have the music up way too loud. If you do try tango, stay away from "ballroom" tango, the real one is the argentine tango.
But yeah, be prepared to be not good at it at the start! It should be ok though, especially if you enjoy it, it wont matter how many moves you can do. It's all about letting go of the thinking mind and just being present to the moment.