I’m pretty sure my son met his girlfriend by searching Facebook for people in our town after we moved here, and sending friend requests – but that was over a year ago, so I don’t know if they’ve changed the rules. I do know that within a person’s own profile, one can choose the setting to not allow strangers to send messages or friend requests.
I don’t think that Facebook is the best vehicle for that, though… I think people would find it a bit creepy. See if your municipality or county has a website, and on there you might find links for other sites related to your region that may have a forum or the opportunity to comment on articles that are posted. Or do a web search for forums related to your particular interests, and once you establish yourself in a community, you could search within it for people from your geographic area, or perhaps even host a get-together near you.
For me, I learned to be less shy and get to know more people by joining Meetup.com, which is a site that hosts groups by region based on common interest, such as hiking; book clubs; fans of different authors, movies, genres, etc.; motorcycle clubs; yoga; urban exploration; pretty much anything you could want. You set up your profile, type in your interests, and search radius for your location, and they will lists groups in that area.
Meetup made a big difference for me. I was living in the same area I’d been all my life, but I had been a single mom with a career, so once my son was grown and my career was established, I wanted to get out of the house. But I only have the one close friend, and I’ve never been comfortable in social situations. I had to force myself out of my comfort zone by reminding myself that most people have some degree of awkward feelings when meeting new people. I had gotten past the point of caring about what others think of me, so I went in with the mindset that I’d be myself and there will be some that I’ll ‘click’ with and others that I don’t. (I learned to do this with dating, too – expect nothing and you won’t be disappointed)