Answer: New York City
We open with actress Ann Darrow, who has recently lost her job, performing at the local theatre and Carl Denham, a director who needs a leading lady to star in his latest film. The two cross paths and Carl offers Ann the role. She initially turns him down, but changes her mind when Carl mentions that Jack Driscoll, her favorite writer, is writing the movie's script. Ann arrives on the ship that will take them to their location, as Carl finds Jack on the ship. Jack hasn't written the full script and isn't coming on the voyage, so Carl stalls him long enough for the ship to leave, starting off their adventure.
The moviemakers did an excellent job of making it look like New York as it was back in 1933, which is the year the movie takes place.