Allowed, almost certainly not, I'm more thinking that she tells her parents she's going to the library with a classmate after school, so they can work on a project or something, and instead wandering around and then going home.

The real problem is, what 11-year-old would want to wander aimlessly downtown and talk to homeless strangers? I'm coming at the permission problem from what I realize is an odd angle: I was taking the subway to school before my twelfth birthday, and I don't think my parents would have noticed if I wandered around midtown Manhattan for a bit before getting on the train home. (When I was in seventh grade my school was in a temporary location a couple of blocks from Grand Central.) I don't remember whether I did wander a bit at that age, but the street grid makes it hard to get lost.