I keep seeing the theory that the NK is going to Kings Landing enough that I think it must be a something of a spoiler - not necessarily an intentional one, but people are hearing it from multiple sources (including, it must be said, just coming up with it on their own because it's a twist when we all are expecting the BoW to be a climactic battle against the NK.)
But my question is like yours - why? If the Night King can create an Army everywhere he goes, by killing people and then resurrecting wights, why go to the trouble of going to Kings Landing? Why not the Riverlands, to pick one closer example?
Just based on the clues we've seen in the previews and show opener (and prophetic images of a frozen Iron Throne), it feels like IF the Night King goes to Kings Landing - a big if - there's some reason why other than just body count. Take the show opener, which now shows the vaults under Kings Landing with dragon skulls, and the Winterfell crypts. We all know some nasty **** is about to go down in the Winterfell crypts - is something also going to happen in Kings Landing where those dragon skulls are? But what, I can't guess. If the Night King reanimates a dragon skull so it can fly around and chomp stuff that will be the dumbest thing I've ever seen.
Edited to add that I think - I didn't check - that one of the skulls down there belongs to Balerian the Black Dread, one of the biggest and most badass dragons ever, and maybe that's important? But it's still just his skull. Like I said, I just don't see how that factors for the Night King. Or anyone else for that matter.