No apocalypse, it was just that crime had gone up significantly. From the opening scene:
Narrator : In 1988, the crime rate in the United States rises four hundred percent. The once great city of New York becomes the one maximum security prison for the entire country. A fifty-foot containment wall is erected along the New Jersey shoreline, across the Harlem River, and down along the Brooklyn shoreline. It completely surrounds Manhattan Island. All bridges and waterways are mined. The United States Police Force, like an army, is encamped around the island. There are no guards inside the prison, only prisoners and the worlds they have made. The rules are simple: once you go in, you don't come out.
How so? New York only claims crime was up drastically, turning it into a prison. No apocalypse level event to speak of, it just looked that way.
Not even LA was post apocalyptic, even as bad as things seemed. Now, after entering in the world code and resetting society with the EMP blast...THAT would be post apocalyptic.