I'd say that the US has about 8 distinct genres of accent: far North-East, Boston, New York City, ghetto, Wisconsin, Midwest, mild Kentucky twang and deep South.
Having lived in the 'DeepSouth' all my life (and having closest to your Midwestern accent myself, unless I have a reason to sound Southern) I could easily say that there are a dozen 'Southern' accents. Where I live now, I hardly notice any accent among the locals, though when I'm talking to someone from elsewhere they always comment that everyone (except me) here has such a strong accent. However when I go back to the town where I grew up I hear a very strong and very different accent from the Raleigh/Durham accent that I'm used to. Likewise, I have friends from other hometowns within a 150 mile radius, and when I hear their parents (or their) accents, they are very different than my parents' and from the 'local' way of speaking. I suppose if you wanted to be very general, you could say that there are just a few broad types of accents. However doing so would leave out vast variations within those categories.
