In my town we had a non-profit literature caffe, it was glorious! In most rooms, we had to keep our voices down, but we could just hang out. Technically, we could order a drink, but I don't think I ever did. There were hammocks, and books. They sometimes organised activities, like conferences and book presentations. It was housed in an old fancy palace, we felt very fancy going there.

I have never heard of a teen library drop-in centre, but I love the idea. With the decline of indoor malls, and especially combined with the brutal winters we have here, there are barely any free indoor spaces for teens or unhoused folk to spend time. Some cities have built beautiful megalibraries (my city is building one now!), and when I've visited them it's been remarkable how free you feel to just exist in the space.