From what I can tell, sickbay is located on the short straight corridor that Kirk and Spock walk down after leaving the Transporter Room. It's the one on the right of the screen:
See how deeply that door is inset? It matches the entrance which we see briefly later on:
You can also see some hallway details which might
match a triangular inersection. Some more are seen later on:
Putting the sickbay set there might seem a bit of a squeeze, but we only ever see the "ward" area during WNHGB. The bit which would become McCoy's examination room during s1 hadn't been built yet.
(As always, click on pics for larger res.)