I don't think "the City" is used exclusively enough in reference to Manhattan that you can fairly call it Manhattan's nickname. It can apply to any of the five boroughs, and you can bet anyone in the suburbs with a son living in Brooklyn will say "my son lives in the city." Hoboken is also a well-known city to the west of lower Manhattan too, so it's a correct answer to that question, and you should probably accept Newark too. "SoHo" is short for "South of Houston." It's not "SoHoSt." I tried "South of Houston" like four times and just gave up. New Yorkers, in my experience say "Houston" much more often than "Houston Street."
Points taken, I‘ll change the city question to something else, accept Hoboken aswell, and accept Houston, but leave Houston Str as the answer that appears, since that is what it actually means. Thanks for the comment