I think Appalachia has, by far, the strongest regional identity in the US. Appalachia has distinct music and art, culinary traditions, and accents and vocabulary from the surrounding areas of the states it cuts through. It has a distinct and unique economic history, which is very much tied to the mountainous/hilly land it occupies. People self-identify as Appalachian, even after moving from it, which is why you see urban Appalachian communities in places like Ohio's 3Cs, Detroit, etc. Cincinnati even has an
Urban Appalachian Community Coalition which works as an advocacy group and resource provider to Appalachians who've migrated to Cincy.
This is quite obviously a deeper connection and cultural bond than what exists in New England, which might have cultural similarities throughout, but would never identify as a quasi-ethnic group like Appalachians do. The South only seems monolithic to people who have never spent time there. There are many sub-regions of the south with major differences between them. Culturally, the low country of South Carolina is extremely different than somewhere like Nashville.