Welcome to the forum!
If memory serves, there are 3 Melkite, about 5 Ruthenian, 7 or 8 Ukrainian, and 2 Romanian parishes in Michigan. If you narrow down your locale somewhat, it may be that some of the members here may be able to give you some insight into the particulars of one or more.
Generally, you'd probably find the Ruthenian parishes to be the most ethnically diverse. Among Melkite (and, I think, Romanian) parishes, it can vary significantly from one to another; both have a few parishes that are more ethnically homogeneous than not. Though Ukrainian parishes vary as well, there are a higher percentage of them that have a strong ethnic presence.
Among the Orthodox Churches that you mentioned, ethnicity is certainly strongest among the Greeks. The Antiochians, like their Melkite cousins, can vary considerably, although they've drawn in large numbers of non-Arabs in the past couple decades. I'd expect that the OCA would be the least ethnically centered of the group, although you might find some older parishes in which its ethnic origins are still strong.