Thanks again for the encouragement from everyone!
Yeah, I pretty much see the deck 2 reference as being dignitaries' staterooms. I would guest that Kirk had Uhura sent the turbolift down to the loop in a holding pattern so that a room could be prepared by the time she got there. Plus there isn't a lot of places to go on deck 2, so there wouldn't really be much of a point for Spock to walk her all the way to the room, specially if her escort would have been waiting for her anyways.
Another possibility is that the Deck 2 reference was intended to be the second-lowest deck within the ship, or the second-lowest deck within the primary hull (since TOS occasionally distinguished between "decks" and "engineering levels"). Although it's likely that the more militarily minded writers and producers of the original series ascribed to the "Deck 1 is at the top" assumption, as hinted in The Making of Star Trek
, going by on-screen references alone, a starship's bridge was never explicitly shown to be on Deck 1 until ST:TNG. (Yes, there's a big "A" on a bridge turbolift decal in the early films, but that need not be a deck identifier, and even if it were, "A" and "Deck 1" need not be synonymous.)
I would imagine that most writers and/or producers not familiar with naval parlance might assume that Deck 1 is at the bottom of the ship, unless told otherwise, following the convention used in many terrestrial buildings.
(For more Deck 1 at the top or bottom fun, check out the first scene of DS9's "Emissary," when the Saratoga
is hit at Deck 1 -- shown to contain the bridge according to interior shots, but seemingly being the bottom of the ship according to exterior shots!)