Yeah, there's the Tangier Island in Virginia where people have an accent that some claim is closer to the English accent spoken in pre-colonial times: https://news.ycombinator.com/item?id=16320595
Some years ago, I read Ben's father David Crystal's book "Pronouncing Shakespeare" and it has a whole chapter on how they reconstructed the original pronunciation. In Shakespeare's time, they did, in fact, write about elocution quite a bit, and some clues come from there. And, as others have noted, you see rhymes and puns show up when you revert to the old pronunciations. As I recall, Crystal claimed that he thinks they got it at least 80% right.
How can you tell the difference between a strange archaic accent and a strange innovative accent?