As the guys have pointed out, there are the two observation deck windows from "The Conscience of the King" and the window from "The Mark of Gideon" which I count as I agree with Mytran that the outside is what Kirk expected to see.
Well, go back to my original comment, and I said "except for those two"... or something close to that, anyway. Those are the only two I know of... well, those two and the "Cage" dome shot.
There is also possibly an early one from "The Cage/The Menagerie" from Pike's quarters that was made into a window in TOS-R but in the original version it appears as a green curved panel.
Yeah, that wasn't a window... for the simple reason that there is noplace on the ship where there could be a windowed wall of exactly that shape. If you're dedicated to the idea of accepting TOS(r) as official, well... let's just call it a high-definition holographical display... which might just as well have been showing a landscape outside of Tucson or a view out a naval vessel's porthole. (Which, for the record, is something I expect every cabin would have... something to avoid the mental issues of being locked up in a cramped tin can for years on end.)
And there has been suggestion that Kirk's quarters in "Mudd's Women" also featured windows but I'm not so sure I can see any stars there. I've included in the reference images below a shot of Kirk's quarters from "The Enemy Within" but the window either has it's shutter down or it isn't a window at all but some wall shelf or something...
I've heard a few people talk about those being windows, but again, I see nothing to indicate those as being windows at all. They COULD be "displays" but they really look more like shallow bookshelves, don't they?
Also, remember, we know that Kirk's cabin is on Deck 5. And we know that there is no way that there could be any window on deck 5, much less one with that angle on it ( since the exterior hull at Deck 5 is a very, very shallow angle in the opposite direction, after all!).
So... we have two windows, plus the "Cage" dome shot. Both window shots are rectangular windows, and only one can be seen out of. And we don't really know just how bright the rooms are supposed to be where these shots are taken, do we?
In terms of the landing bay's observation gallery... I'd fully expect the lights to be dimmed, if not totally off, when Kirk is taking his conquest on her "tour." It's worth noting that there ARE two windows in "approximately" the correct spot in the model...
Since I don't feel like doing any new renders or so forth right now, I'll just toss out a shot of my model I've already created, which just happens to very effectively show the location of these two rectangular windows relative to the hangar deck.
And I expect that the window we see in "Gideon" is in the dorsal... probably the starboard side (port shown here, by the way), second row from the top, near the aft edge of the dorsal: