The city of the Machines is known simply as 01 (sometimes Zero One, or the Machine City).
It was created long before the events depicted in The Matrix, when humanity spurned the machine communities' desire to become partners of man (with the same rights and freedom). 01 became a prosperous and peaceful city, selling goods to humanity's countries. It is actually located in the Arabian Peninsula, south of the Fertile Crescent.
Man's economy lost revenue and, as a result, power. They used nuclear weapons in an attempt to destroy 01, and thereby eradicate machinekind. These weapons proved to be ineffective against the machines. War machines developed in 01 advanced throughout the world, invading human nations. This led to the scorching of the sky and the downfall of man.
Without human intervention, 01 has grown to tremendous size. It runs on a combination of nuclear fusion and neuro-electric energy generated by the billions of humans in its power plants, which are connected to the Matrix. Surrounding the city is an immense defense system consisting of large, crablike Defenders that activate when unauthorized craft approach.