Behind the curtain is the best bet - we see where the other door goes and we get a pretty good look of Spock's cabin throughout the rest of the episode.
But in any case, there were never intended to BE bathrooms adjacent to the cabin set. As seen here: http://www.startrekhistory.com/DS4.html
that door was meant to be a decent sized closet. Sadly that scene ended up on the cutting room floor, but it does jive with the overall utlitarian feel of the ship. Plus, no-one bats an eylid when a shirtless captain goes striding through the corridors (on his way to the bridge, no less). Might this suggest that there's nothing unusual about officers and crew strolling around the hallways to get to the nearest washroom? Given the (supposed) ease at which the crew of this futuristic have around each other physically, it is certainly a possibilty.
If true, it also clears up an oddity in Elaan of Troiyus
. Here, Uhura gives up her quarters for the spoilt little princess. What's so special about these quarters? Yes they have some nice drapes and lots of breakable objects but is space on the Enterprise really at such a premium that NOWHERE else could be made available? Quote a departure from Journey To BabelI!
Fortunately, the episode does provide an answer, for at one points Elaan locks herself in what is almost certainly an ensuite bathroom. So, what's that doing there? Uhura could certainly charm a few of the technicians back in Man Trap
to do her bidding, and as a high ranking officer would command the authority to have the empty space adjacent to her cabin into a personal toilet area. On the Enterprise, this would be an unusual feature. So unusual in fact that Uhura may have been "volunteered" to give up her sanctum for the visiting dignitary.