So not so long ago I proposed origin techs for each civilization, such as "Homeland Africa", "Homeland Asia", etc. I am thinking of revisiting this idea but with with new Unique Buildings. For instance let say we have with the core civs ...
Culture
Req Tech: Cultural Identity
Cost: ?
Bonus: Can Build "X Embassy" Twice as Fast
Thus if you are Greek you get Culture (European) as your unique building and it will allow you to build any of the European type embassies twice as fast as non-European civilizations.
The other potential of having a culture building is that Assimilation will actually have a use because if you take over say a Japanese city then that city will have a "Culture (Asian)" building rather than a "Culture (European)" one.
Note I could always change the name to "Ethnicity" instead of "Culture" if you guys don't think the name fits.
EDIT: The other thing i could do is make one for each individual civ and just have their effect based on the closet cultural groups. Such as Culture (British) could build the American Embassy faster even though its under the Americas.