When I was growing up in the Chicago suburbs, it was always a treat to go downtown for St. Patrick's Day or the days surrounding it, to see the Chicago River dyed a deep green. I think they still do that, but at the time, the mayor was Irish, as was his son who was later elected mayor (Richard J. Daley and his son).
For years I could not figure out why Mayor Daley didn't have a musical Irish accent, since he certainly had a pronounced Chicago accent. I finally supposed he had grown up in a patchwork of immigrant neighborhoods where the accents had all run together -- Irish, Italian, Polish, Yiddish and many others -- resulting in a sort of Chicago brogue distinctive to the place. He really chewed on his consonants.
When I was commuting downtown to my undergraduate underclass years of college, a kid with a true Chicago brogue asked me if I was a foreigner. I think I had some of my familial New England in my speech, plus a lot of the leveled out Midwestern enunciation, now oddly transfigured by years in Missouri, California, and the American South. All I can say is that Southerns never mistake me as native, ever, but when I tell Chicagoans I grew up in their area, they say, "With that Southern accent?" Such is life.