Re: Next steps...
You could of course just surface one of your submarines in New York/San Francisco harbour and set the nuke off. Bit hard on the crew, admittedly.
But any delivery mechanism where you have to drive/sail the thing to its target creates many problems and uncertainties. Especially when you're a rogue state, that doesn't have normal access to global shipping routes, and so who's stuff is at high risk of getting inspected/found.
Plus you've got massive command and control problems. Once the warhead leaves its borders, the regime essentially has lost direct control of it. And paranoid family dictatorships aren't known for their high trust in subordinates.
Plus, where would they keep the thing in the meantime?
The North Korean airforce aren't expecting their planes to survive long enough to deliver these nukes, and I suspect the navy fare little better. So ICBMs are the most reliable means to work on. And North Korea has had a decent missile program for a while - it was missile tech that the Norks swapped with Pakistan to get their nuclear tech after all. So it's a natural fit. Plus it's also the scariest option, as well as making the regime look more poweful inside its borders. And propoganda is at least as important as reality, to a regime that only survives on fear and brainwashing.