You're having fun putting elements together, and this is good.
Mujer neoyorquina is certainly possible; note that here, "mujer" is a bit redundant, so you might prefer the simpler version, without "mujer": neoyorquina, e.g. "As a good New Yorker, she some some specialty side dishes from the neighborhood deli" | Como buena neoyorquina, etc.
Demócrata washingtoniano could work in some circles, but note that when people speak in English about Washington Democrats, I don't think they mean a special flavor of Democrats, which is what "Demócrata washingtoniano" suggested to me. I think they mean Democratic members of Congress (los demócratas en el Congreso). Also note that "Washingtonian" has a special meaning to people who live in DC. It refers to the local culture of that area. Which I don't think is quite what you were aiming for. I think you were trying to do something similar to "neoyorquino," no?
If I go back to your title, Noun Adjuncts associating a noun with a place -- hmm. Let me see if I can construct an example.
Women who live in the mountains, or mountain women, could be mujeres de la sierra, or more succinctly and commonly, "las serranas", e.g. "Las serranas de los lugares aislados generalmente se lavan el pelo en el río."