My impression is that the regionalism varies a lot depending on the size of the region. While I'm a proud Californian, I have more pride in my Bay Area roots. California is a big place, and has several really distinct locales with distinct cultures. My impression is that folks from Wisconsin tend to think of themselves that way: Wisconsin is the unit (and has a bit of a chip on its shoulder). Ohio is probably big enough to have several distinct places that people think of themselves as from. NYC is very different from upstate. Boston is different than anywhere west of Boston in Massachusetts.
Texas appears to have a curious statewide affect, despite it's size, but I'm sure there are intrastate rivalries. I think I've heard that Miami is fairly distinct from the rest of Florida, but maybe I'm wrong. I suspect Georgia is kind of Atlanta and not Atlanta--I bet that's true of a lot of states with a big urban center, and large more rural areas. Certainly within Wisconsin, Madison and Milwaukee are distinct from the rest of the state.
