The strangest accent I ever heard was in Eastern North Carolina. They sound almost Cockney
Coincidentally, a lifetime ago in college a visiting prof from NC filled in for a lecture. After a while, I kept thinking how very English he sounded. It was so distracting that I paid no attention to what he was saying.
Then again, there was nothing new there.
That may be the Okracoke accent of the Outer Banks -- "Hoi Toid" for high tide. There are some very distinctive dialect pockets in Eastern Shore Maryland, and along the Virginia Coast, as well. Some people on islands and inlets had little contact with the outside world and preserved older dialects, like those in the hollows and coves of the Appalachians.
I knew someone who sort of munched his words in an incomprehensible, though vaguely British fashion. It turned out that he was from Martha's Vinyard. They work on keeping up their distinctive accent in the Winter when the tourists are gone. Apparently Vineyarders also have a distinctive "dialect" of sign language, since there was a deaf colony on the island.
Here's a page on regional accents. It puts a lot of stress on what the local dialect word for "doughnut" is for some reason.