All good things must come to an end, and while the season 3 finale of Stranger Things wasn't as much of a closing chapter as it seemed, the episode did see major players the Byers family and Eleven uproot and leave the small-town setting of the show.

Where did the Byers move?

Conclusion: Murray will be back in season 4. The Byers will be living in Illinois - someplace in central or southern Illinois, not up around Chicago, and the Byers will be close to/in contact with, Murray.

Do the Byers move away?

The Byers family and Eleven move out of Hawkins, Indiana. The Russians have a Demogorgon (and a mystery American prisoner) in their captivity.