Well, after finally seeing the movie, I can say with confidence
that the Atrium does go down the center of the saucer, and that the dome at the top is the large one above the bridge.
Looks like that the the rear wall of the bridge butts up against the opening/shaft.
See Link/Picture below for reference.
King Daniel wrote:
Click here for diagram
. My idea of where everything is. The positioning of the shuttlebay, engineering, bridge and plaza is concrete although the sizes may be a little off. The turbine placement is based on the zoom-in when Kirk and Scotty transwarp-beam over in STXI, and the curved ceiling where they materialize. Communications (where Kirk found Uhura in STXI) is located behind the deflector dish, as per Chekov's dialogue in Into Darkness
. I'm guessing the new warp core is next along from the shuttlebay and engineering. We see them launch a ship from shuttlebay 2 in Into Darkness