New York is far from the largest city in Medieval America, but right now is thriving as a strategic military outpost, and no doubt a symbol of prestige.
In the Industrial era, New York City was the de facto capital of the western world. A center of art, finance, and a gateway to the rest of the world. After the collapse, the city could not empty out fast enough. There was no way to feed its teeming millions. most major corporations were defunct. There was no immigration center, or tourism industry. For centuries, the giant glass skyscrapers were more of a liability than anything. Central Park was a good place for outlaws and refugees to congregate, but the concrete jungle was effectively a mausoleum.
After several centuries, with every skycraper that was going to collapse collapsing, and every tunnel that was going to flood having flooded, mariners from the United States found the skeletal canyons of the city to be an almost concentric series of walls. Actually, this was noticed by the armies of the splintered New York kingdoms, but the United States were more effective at taking the city and utilizing it as a labyrinthine fortress. Many of the historic names for places remain, in theory, but used for much different purposes. Rockefeller Center is the seat of government. Times Square is where executions or corporal punishments are held. Central Park is a game area.
New York City is primarily just Manhattan, however a few garrisons exist on the outer boroughs, and the cliffs overlooking the Hudson. Also, the villages and estates that dot Long Island are pretty much under the jurisdiction of the army, when not under the United States itself.