What kind of "shared" office space am I specifically looking for (don't know what it's called)

I live in St. Louis. I’m a freelance editor for fiction, and I also work remotely for a publishing house (for non-fiction). Because I work at home I get pretty lonely in an isolated environment. I’ve tried working at my local library, but it can be a pretty sad place; there are mostly homeless people trying to find shelter, or middle schoolers being noisy.

What I’m really looking for is a place where I can rent out a desk in a shared office area, but not one that is too corporate. I’m a young adult, and I love being around hip places. I dress pretty casual, and I love being around other individuals my age who might be in a similar position as me – or groups of people who are working on small start-ups.

I’m originally from the Bay Area, so I know there are places that “exist” where individuals or small groups can share an open space and set up cubical areas where needed – I just don’t know exactly what to search for when it comes to other places outside of start-up land…

Would any of you guys be able to help me?