National City and Metropolis are about 2700 miles apart (assuming National City is LA and Metropolis is NYC)
New York City is separate from Metropolis and Gotham City in the DC Universe; it's where the Teen Titans were based, for one thing. The
Atlas of the DC Universe put Metropolis in Delaware.
Smallville put it in Kansas so it'd be close to the title location. Siegel & Shuster originally based it on their hometown of Cleveland, and the 1950s TV series basically treated it as Los Angeles, where the show was filmed. I think the identification of Metropolis with NYC may have started with
Superman: The Movie. Traditionally, the DC city associated with NYC was Gotham City, whose name is a nickname of NYC.
In the Arrowverse, we know from
Constantine and
Legends of Tomorrow that New York City exists on Earth-1. And it
used to exist on Earth-X, before the Nazis bombed it. However, it hasn't been established whether it exists on Earth-38. And there's no mention of an Earth-1 Metropolis to date. We do know of a number of cities that exist on both E1 and E38, though: Gotham, Central City, Star City, Opal City, London, Paris, and Beijing.