A story which features culture-clashes or other new and interesting aspects of the culture(s) of that universe.
Putting on Civvies (Star Trek: Reboot) by Tree and Leaf
Vulcan has three second-person pronouns. (pre-Movie, Spock, Uhura)
Mixed Signals (Stargate/Sentinel) by Lori Wright
This is a Xover between Stargate and The Sentinel. When Blair Sandburg unknowingly shows a member of the SGC a picture of Egyptian-like ruins found in a dig in Peru, it causes an avalanche of circumstances, which forces Jack O'Neill to head a mission to Peru.
(2) The Benefits of Rigid Thinking (Star Trek: Reboot) by Mariole
Kirk is directed to return some stolen artifacts to New Vulcan - but of course nothing goes smoothly where Vulcans are concerned.