Though never mentioned by name, based on information from The Animatrix (2003) the Machine City is actually called "Zero-One" and located in the Empty Quarter in Saudi Arabia. This, as well as Zion as the last human settlement, would imply most of the main action of the film franchise takes place in the Middle East.
The Matrix Revolutions
The human city of Zion defends itself against the massive invasion of the machines as Neo fights to end the war at another front while also opposing the rogue Agent Smith.
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