George Clooney was born and raised in Kentucky, and you can still hear a slight Southern twang when he speaks.
Fran Drescher (who starred on the TV series The Nanny)has a very pronounced Queens, New York, accent. (In describing it, folks might say she has a "Noo Yawk" accent.)
Of course, most celebrities that crave a successful career in acting or broadcasting (in the US, anyway) work hard to lose any trace of a regional accent and strive for a traditional flat, Midwestern pronunciation. (Have you ever seen the sitcom Home Improvement? Tim Allen was born and raised in the Detroit area; his is a good example of the Midwestern accent.)
If you ever watch re-runs of Cheers, it's interesting to note that although the show is set in Boston, the only character that has anything close to a traditional Boston accent is Cliff the Mailman.