Someone has created an AI of human-level intelligence, and within hours this AI has grown in intelligence and power to the point that human life no longer seems so sacred. In an instant, all life on the planet is extinguished, and the AI begins to rebuild the Earth in a way that best suits its needs.
What I'm wondering, though, is how this AI would build its capital city. Let's assume that it has the same problems computers have today: the need for a lot of fast processors, a lot of storage, a solid connection to other nodes in the system, easy access for maintenance and repair, and other such things. Let's also assume that the combined size of the AI and all its components rivals that of a small city. What would such a construct look like? How could it be shaped, and how would it efficiently solve its myriad problems?
I know there are modern-day examples, like with server rooms and the like, but I'd think that an increase in scale would require some more interesting solutions.
EDIT for clarification:
By 'city', I mean mostly just a big datacenter, where the AI can think and remember things. Also included should be all the systems necessary to keep this datacenter running, from power systems to maintenance robots.
As for resources, the AI has control over the entire Earth, so anything that's on the planet and can be gathered using modern technology is fair game.