If it were me, I’d go with Riverrun 2.0.
Sorry, just to be clear: a long-term Kingdom of the North and the Trident would need two capitals that the monarch alternated between. Riverrun 2.0 is a good idea, both for strengthening the monarch’s hand vis-a-vis the often fractious Riverlords, but also because it’s a pretty straight shoot from there to White Harbor and thus to Winterfell.