Shhhhh! This is a library!
Isn't this the stereotype? Libraries are quiet places for independent reading and study, not places of for socializing. Libraries certainly can be this if you want them to be, and I'm sure some libraries are filled with cavernous silences. But that is far from true in many, if not most, modern libraries.
Libraries are often hubs of activity. Libraries are often sites of public lectures on any variety of topics. They also often host public forums. You can usually find a bulletin board posted with flyers and announcements of community events. Lots of public libraries also host reading times for children. If you're lucky, you may even find authors stopping by a library to read from their own books.
Informal discussions also abound. Want to discuss books? Librarians are often happy to talk with you, when they're not busy, of course. Do you see people browsing through books you've read or perhaps the recent additions? Strike up a conversation. Most people are happy to converse. You already know you share an interest in books; just take it from there. It's social the way social was always meant to be.
I haven't even mentioned clubs. Many libraries have book clubs. There are books clubs for adults. There are books clubs for youth. There are manga clubs. Given that libraries have now become digital hubs as well, there are clubs for online and computer gamers. Even non-media clubs such as boy scouts and quilting guilds meet at libraries. It's truly a community center.
I've heard people say that once they're out of school, bars and churches tend to be the only places to go and meet people. I beg to differ. Make your local library a new habit. It was the original social media source.