I am also interested in the explanation. I have a guess but would like to have it confirmed: burada -> sit as in "why have you been sitting here", buraya -> sit as in "why did you seat yourself here?"
If that is correct, I think the (one) correct translation of "Neden buraya oturdunuz?" could be "Why did you seat yourself/yourselves here?"
I think in the meantime I have learned enough Turkish to answer my own question :) The nuance between accusative & dative case is:
1) Neden burada oturdunuz -> Why were you sitting here?
2) Neden buraya oturdunuz -> Why did you sit (down) here?
I did not translate the tense correctly, in order to make the difference in meaning clear. The correct translation in both cases is "Why did you sit here?"
Yes. The "locative" ending "buraDA" indicates a stationary state (someone currently sitting there), while the dative case indicates a movement toward something (someone in the process of sitting down somewhere)
I just found that the wikipedia page on Turkish grammar seems to be very good.. Never spotted this until today: https://en.wikipedia.org/wiki/Turkish_grammar#Case
@blainluckyk, burada has the locative ending -da, where buraya has the dative ending -(y)a. It's a distinction like German hier/her, Esperanto ĉi tie/ĉi tien, archaic English here/hither, etc. The confusing part is why this sentence uses the dative; it doesn't show movement toward something but a location.