For years I've wanted to do it. Get in the last car of the 6 train at City Hall/Brooklyn Bridge, the last stop of the downtown local.
Act like a tourist who doesn't know better. The train loops around to the uptown side by going through the old City Hall station, which has been closed for decades.
OK, well, you can't see all that much of the arched station from the train. Better views in the link above. But the train did stop, allowing this view through the window.