Define "regional culture". Do you mean accent? Do you mean a unique language? Do you mean a dialect? Cuisine? Dress? Politics? Religion?
Many (or most) native American communities (particularly reservations) have distinct languages, religion, culture.
Utah has lots of Mormons who all speak pretty standard English but have some unique cultural ideas and dress, in some cases.
Brooklyn is full of Hasidic Jews.
A lot of people in the state of Hawaii, even if not native Hawaiian, speak pidgin.
There are lots of religious sects that have distinct cultures. The Amish all speak English but some Mennonites speak Dutch-German.
I hear that people from Maine are all wacky and speak funny.
Appalachian communities go back to Scottish settlers and are widely thought of as a distinct American subculture.