Your library might have a crafting club that you could join, even if you're not a big reader. Or they might have ukelele concerts or mahjong tournaments or other activities like that. A lot of libraries are running different events to bring the community in. They'll also have noticeboards for community groups and meditation clubs etc.
I'm not sure how to find a good LGBT social group - there are some counselling services listed by state at ReachOut. (
http://au.reachout.com/lgbtiq-support-services ) Perhaps contacting one for your state and asking them about LGBT social groups in your area might be a start?
