In the episode Voy: Repression, I noticed that when Captain Janeway is escorted into the Ready Room to be executed by Tuvok, she comes through a second door.
Where does the second exit in the Ready Room lead?
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It seems to lead through a small ante-chamber back out into the corridor that runs behind the bridge.
Presumably there will be times when you want a crewman to attend the Captain in the Ready Room but without them having to go through the Bridge first.
You can also see the (unlabelled) exit in the original set plans, sold in the "It's a wrap" prop auction.
I have to disagree with @Richard (!)
From the schematics of Intrepid class ships, available e.g. here we get a different picture. Here's a blowup of Deck 1:
The other door in the ready room leads into what looks like a personal head / shower room, which I believe makes more sense than an exit to a hallway. At any rate, there's no access from there to the turbolift, it seems.
You can also have a look at this version of the Intrepid-class schematics for the U.S.S. Odyssey.