Will and Eleven move away at the end of Stranger Things season 3 because Joyce decides to leave Hawkins for a safer, fresh start after everything her family has suffered there, and Eleven goes with the Byers because Hopper is gone and Joyce effectively becomes her guardian. Their move is both practical (escaping danger and trauma in Hawkins) and emotional (trying to rebuild some kind of normal life together).

In-story reason they move

  • Joyce has watched her family go through repeated supernatural trauma in Hawkins: Will’s abduction, his possession, Bob’s death, and finally Hopper’s apparent death at the lab, so she chooses to get them out for their own safety and sanity.
  • Hawkins has become a place full of awful memories for the Byers, so leaving is framed as a chance at a fresh start where they might finally live a “normal” life.

Why Eleven goes with the Byers

  • After Hopper is believed dead at the end of season 3, Eleven effectively has no legal family of her own, and Joyce steps into a mother-figure/guardian role for her.
  • Eleven has already been closely bonded with the Byers and is treated as part of their family, so she naturally leaves Hawkins with them when they relocate to Lenora Hills, California.

How the move plays out in season 4

  • In California, the Byers and Eleven try to build a normal life, but it does not turn out to be the safe, happy reset they hoped for, as the Upside Down–related threats eventually catch up with them again.
  • Eleven also struggles at her new school, facing bullying and isolation without her powers or old support system, which shows that “moving away” didn’t magically fix her problems.

TL;DR: They move away because Joyce wants to protect her family from the danger and trauma of Hawkins, and with Hopper gone, Eleven becomes part of the Byers household and leaves with them to start over in California.

Information gathered from public forums or data available on the internet and portrayed here.