Spoilers ahead for Stranger Things 3. Though Joyce gave no indication of where she, Will, Jonathan, and Eleven were headed when they left town at the end of Stranger Things 3, if you dig far enough back in the show, there are a few clues that the Byers are moving to Maine. In fact, while you may have missed seeing his face onscreen, you can probably go ahead and blame the whole thing on Bob Newby.
Before his death in Stranger Things 2, Bob brought up the possibility of moving to Joyce not once, but twice. The first time was when the two were dancing to Dolly Parton and Kenny Rogers in "Trick or Treat, Freak," and he proposed she and the kids move to Maine with him. "What if we were to move out of Hawkins ... together?" Bob asked. "My parents are selling their house in Maine." He even had a plan to get a job at the local RadioShack.
Then, after the Mind Flayer had taken control of Will in "The Spy" and Bob found out the extent of what the Byers had been through, he brought up the idea again. "It kinda makes my idea of moving to Maine sound a little less crazy, right?" he said to Joyce. The first time, she wasn't too interested, but upon realizing the Upside Down still had a hold on Will, her tune had changed. "Oh, it's not crazy at all," she replied.
In Stranger Things 3, of course, Bob was already dead, but perhaps the thought of moving to Maine didn't die with him. It seemed like there was a chance Hopper could convince Joyce to stay in town, but after his supposed death — plus all her bad experiences in Hawkins and in her own home (seriously, the Byers' house has gotten beaten up nearly as many times at Steve) — Joyce just couldn't find a reason to stick around.
Based on how sad Mike, Dustin, Lucas, Max, and Nancy were to say goodbye to the Byers, it seems clear they're going somewhere far away. And as Indiana is more than 1,000 miles away from Maine, the Vacationland state fits the bill. Plus, Maine makes sense because of its connection to Stephen King. Most of King's stories take place in his home state of Maine, and he's had a clear influence on Stranger Things: references to King's body of work have been sprinkled throughout the show from the beginning. The Duffer brothers even told IndyStar in 2016 that Hawkins was inspired by King's fictional town of Castle Rock, Maine.
As for other potential locations that the Byers could be moving to, the Duffer brothers originally set Stranger Things in Montauk, New York, and the show was even called Montauk. (This has caused some legal trouble for the brothers recently.) They told the A.V. Club this came from their love of Jaws, since the book was set in Long Island (the fictional Amity was moved to New England for the Steven Spielberg movie). But they switched gears to the Midwest after a coastal setting became too expensive.
Since Stranger Things is now a massive hit, Netflix might be willing to splurge and move at least some of the filming to the East Coast. And between the ocean views and the eerie, remote wilderness, it's kind of the perfect place for a show that likes to contrast a small, idyllic setting with lurking danger. Hawkins may be still be the home core of Stranger Things, but don't be surprised if you see some of the action moved to Maine in Stranger Things 4.