Appleseed Alpha Vol 1

From the Kodansha edition

In the 22nd century, New York City is a war-torn place ruled by warlords and a giant robot mayor with three eyes and a three-piece suit. While there, Deunan and her cyborg lover Briareos stumble across two citizens of a legendary utopia. It's up to them to guard what could be humanity's best chance to rebuild.

Source: Anime News Network Encyclopedia