While the Tudor City scene does nothing to advance the movie's plot, it chillingly illustrates Bickle's precarious state of mind. As the scene begins, the cabbie picks up a fare in front of McAnn's Bar and they proceed to Tudor City.
The cab drives up 41st Street past the South Park. . .
. . .and stops in the cul-de-sac adjacent to Tudor Tower. (The corner store, today Conran's Bike Shop, was then a Thomas Cook travel agency.)
It's quickly apparent that the passenger (played by a jittery Martin Scorsese) is completely deranged. He tells Bickle that his wife's having an affair with a man in a Tudor Tower apartment.
. . . the passenger's wife, languidly smoking a cigarette and gazing out at the lights of the United Nations.
See the full, R-rated sequence here.