It'd surprise me by not falling into the story loop Zelda games have used many times before. I'm just not interested in the same story cycle that games like Ocarina of Time, Twilight Princess, and Skyward Sword go through. To me, Zelda games have reached a point where they're so predictable from a narrative sense that you could watch the first five seconds of every cutscene, skip the rest, and still know exactly where the game is going.
I harp on it a lot, but I do think Breath of the Wild was a powerful step outside the box for a series so entrenched in its own box that it was beginning to suffocate. Breath of the Wild was about a Link who lost, a Hyrule that was burned to the ground, and a Ganon just mindlessly hovering above a battlefield it's long since conquered.
For Breath of the Wild 2 to surprise me, I'd want it to twist the game's premise at least a little bit. If I were writing the story, I would kill Link. No resurrection or quest to restore his. Link is dead and Zelda, the new protagonist of the game at long last, must move on. She's not physically adept at martial combat like Link was and what vast magical power she did have is waning.
I'd also like to do something interesting with Ganon for once.
Ganon has never been a developed villain. For a series as longrunning as Zelda, no entry has ever tried to make him look like anything more than some mustache twirling villain. I know that folks will point to Wind Waker, but he had, like, two sentences worth of dialogue in that game about some vague motivations. Ever other game just features him kidnapping women, laughing maniacally, and playing a piano.
While it became kind of a meme after Ganon's appearance in the BotW2 trailer, I'd like to see the Good Guy Ganon trope. Perhaps the looming threat isn't just Ganon for the twelfth time. Maybe a game where Zelda and Ganon, previously enemies in all other installments, work together.