The social maps and personal quarters maps aren't really things you can "play", at least not usually - they're just stage sets for role-playing with friends, there are no tasks to be done. As such, you'll find a lot of them under the "Review Content" tab (you need to enable reviewing in some way to be able to access that, I forget how but I don't remember it being hard to find when I did it). There are also some in the main section, ie. "Borwse All" - searcch for missions wit hte "Quarters" tag, but check the descritions too as some missions seem to have been given that tag wrongly, probably some players didn'ty undestand what it meant.
Comments
There's one called "Romulan Zoo" or something like that.
Foundry Mission Database
Check out my Foundry missions:
Standalone - The Great Escape - The Galaxy's Fair - Purity I: Of Denial - Return to Oblivion
Untitled Series - Duritanium Man - The Improbable Bulk - Commander Rihan