Where else for a Hegemony but Ribeirão Preto, Brazil
I remember that, in one of those '70s futureouter-space-fantasy illustrated books I enjoyed as a kid, they had an interplanetary spacecraft take off from Darwin, in northern Australia. For some reason, I think that would work well.
I also like the already-mentioned Singapore, Pyonyang, and Zanzibar.
Probably figured there could be no reasonable option than the obvious…
…Scientology?
Zoroastrianism?
We’re sorry. The correct answer was Mormonism.
What? But y’all never follow the rules I set down in MY insane hypotheticals!!
Admittedly, I don’t either.
You know, I’m not sure where I was going with that.
France just announced secession.
Obviously, the world capital must be at the site of the Space Elevator. Since the space elevator must be built on the equator, and at a high altitude, the obvious capitol city therefore is Quito, Ecuador.
How about Puma Punku? I mean, since aliens built it and all, seems like it would be a natural…
-XT
The British moved the government of India twice a year between Delhi and Simla
Argentinians my ass! We Peruvians would never stand for a guy named Santiago to be close to the building, let alone the city. 
Also, it’s got air pollution like hell.
Ayers Rock
Could we rotate it around every ten years or so? We could have each of the world leaders draw straws?
Not if it’s a working capital–i.e., the center of the world’s government, with a capitol, executive mansion, bureaucreatratic offices, and so forth.
If it was a flying (and submersible) artificial city, you could rotate it any time you wanted.
(Well, any time Maximum Leader Zombie Freddy Mercury wanted).
I, for one, welcome our undead musical genius overlords.
I believe you forgot to add the adjective “flaming” to Pres. Mercury.