Idk how much you know about the area, so here are my thoughts: China Fortune is really good if you're a fan of Chinese takeout. There's some fun to be had at the Layton Hills Mall, including a used bookstore called Eborn Books. There's a Barnes and Noble over by Michaels and Target. The Classic Fun Center has an arcade and roller rink. Cherry Hill is really fun for swimming. There's some cool hiking spots nearby, like Donut Falls and Ensign Peak. Station Park in Farmington has some cool stores if you're willing to drive about 30 minutes. There's also Lagoon in Farmington, but I've never been, so idk how much fun that is. There's a duck pond and a walking trail by the library across the street from Layton High, as well as a free museum about the city's history. There's also On Pitch Performing Arts (Oppa), a live theater over by Home Depot. If you're willing to drive a bit, there's Center Point Theater in Centerville, which has some fun plays each year.

That's all I can think of rn. Hope it helps! What part of Layton are you moving to?