Yes they do actually. It is more distinctive in some places than others. I listen for ruf for roof, and Warshington for Washington. It is obvious in Minnesota, Wisconsin and Chicago, but I can tell an Iowa accent too, often. It just has a certain je ne sais qua. The UP in Michigan has a near Canadian accent. Detroiters have a certain flat quality that I cannot quite describe. Few sound like northeastern seaboard types, even those without much of an accent, like my Dad.
Where I fall down, is when it comes to the South. They all sound the same to me. I can't tell a Virginia accent from a Texas accent, and that's pathetic. But then I am a Yankee. :)