Originally Posted by Captain Tom Coughlin
It seems to me like everything that looks like a room is in the saucer section and the neck, and the secondary hull where engineering is located (this is where Uhura was) is a wide open space.
We don't know that Uhura was in the secondary hull. If you'll watch that scene, Kirk and McCoy leave sick bay and go directly out the door to a computer terminal. Kirk locates Uhura and they both run from the terminal straight down the corridor to the room with the big tanks where uhura is. I will have to watch it again to be sure, but I don't think there was a cut in that scene. Therefore, the room Uhura was in was on the same deck as sick bay.