In the Stupid Ages, Old New York was known as simply New York. It was one of the biggest cities in the world and produced more garbage than any other city. In 2000, the city put its garbage on a giant barge, which was launched into space 52 years later.
The remains of much of New York still exist as ruins in the 31st century, due to the attack by Bender, below the streets of New New York. They may be part of the New New York sewers.