Linguists have figured out what the accent in Shakespeare's day would've been based on contemporary writing. I believe the document that tells us the o in "prove" is the same as "love" and "brother" (what makes the last two lines of Sonnet 116 rhyme) was from the 1620s.

Meanwhile, Harkers Island, NC was settled in the 1730s and it and the nearby islands still have their own distinct English dialect not found on the US mainland, thanks to geographic isolation. The High Tider accent matches up pretty well with the Shakespearean one, exempt from the later vowel shifts that occurred in both North American and Britain. That's probably the closest thing you're going to find still being spoken.

You'd probably have difficulty understanding it if they got actors to speak with it in movies, depending how strong they do the accent.