My wife Lesya and I are both Ukrainians. However, since there aren't any Ukrainian Orthodox parishes anywhere near where we live, we go to Fr. Chris's Greek Orthodox parish in Aberdeen, MS.
Our impression about this little mission parish is extremely positive. Not once were we asked, "what are you doing here as you are non-Greek?" Our co-parishioners include 100% ethnic Greeks, half-Greeks (children of mixed marriages), and non-Greeks, and we all get along very well!
The Divine Liturgy at our parish is mostly in English. Only occasionally, Fr. Chris chants some liturgical exclamations and prayers in Greek; but that does not bother us, non-Greek speakers, at all because we all have booklets with parallel Greek and English texts of the Divine Liturgy. To me, actually, it is even a peculiar pleasure to hear lines from the Divine Liturgy of St. John Chrysostomos in the language it was originally written.
Sometimes, I hear from people who are usually of an Anglo- descent that Greeks aren't friendly to them when they come to a Greek church. I simply cannot relate to that. Again, my own impression was so positive that it is even hard for me to imagine, why would Greeks be un-friendly to someone who is not Greek.
Maybe it helps if you show interest in the Greek culture, language etc. When Lesya and I first showed up in our parish, we both asked some Greek parishioners about their place of birth (you know, Greeks just LOOOVE to talk about THEIR particular island!
), asked how to pronounce certain Greek words. I guess that made us rather likeable to the parishioners who are Greeks.