Manfield, capital of Mankind, first global president Steve McManaman.
Moscow would be good, nice and central. Delhi, maybe, please the non-aligned fellahs.
Feminists would love it!
What about auninhabited pacific island?
Equally inconvenient for everyone, small in size, necessitates a drastic change in world greenhouse gasses (after all, how silly would it look if our world HQ was put under six inches of water… Everything would be soaked!), and best of all, no bitching about favoritism.
ETA:
Small in size is a good thing, IMO. Big enough to have government offices, small enough to prevent a shit load of lobbyists and tourists from frequenting the place.
Maybe Stephen Ladyman, formerly Transport Secretary, rather than Steve McManaman. Compromise, you know. God created man, male and female created he them. So Mansfield. Maybe Mansfield Woodhouse.
Atlantis!
Katmandu is right between the two most populous countries, and the altitude would allow the new government a metaphorical basis for describing itself as the world’s highest authority.
A giant flying artificial city.
That failing, Zanzibar. Because it has the coolest name. Plus, Freddy Mercury could be brought back from the dead as Permanent Maximum World Leader.
A giant flying artificial city that can also submerge or float like a submarine - Stargate Atlantis!
because you know, by the time we need an answer to the OP it’ll be possible.
Karachi, Islamabad or Tehran are the closest major cities to the center of population. Kathmandu isn’t really all that far off.
I don’t see what’s wrong with Brussels. They’re already working on it anyway. 
The UN is actually pretty small. We stayed at the Millennium Hotel there last month and the complex is smaller than your average suburban high school (though with more room thanks to the high-rises).
'Course, if you include the permanent missions/consulates dotted around the surrounding area, it’s pretty big.
Bilderberg also isn’t a boys’ club, or at least no more so than any other meeting of world leaders and business magnates. Queen Beatrix of the Netherlands, Hilary Clinton, Maggie Thatcher (before she was Prime Minister), and Condoleezza Rice have all attended.
Easter Island. The politicians will feel at home with all the big heads standings around.
You think it’s expensive to run the US government from DC? Try running it from Hawaii…federal wages would have to probably double, at least, just to cover cost-of-living.
To make the government appear un-Eurocentric as possible and thus satisfy Africans and Asian Third World nations.
Right rationale, wrong pole. Antarctica gets my vote. It’s already owned by a bunch of different countries. Also when the snow melts we might find Atlantis underneath.
Or the cities of the Elder Things…
Tekeli - Li! Tekeli-Li!
(bolding mine)
Is it your intent that the government in fact BE Eurocentric (or perhaps American-centric), regardless of appearance?
It will be a Western-style democracy with English as a lingua franca so this might be an area to compromise on without fundamentally threatening the government.
Why are you assuming a world government would be constituted thus? Whose to say it’s not formed at gunpoint by the machinations of a super power who achieves dominance over the rest of us?
Besides, assuming it is a western-style democracy with english as the main language I hardly think putting the capital somewhere outside Europe/the US is going to mollify complaints that it’s culturally biased.
Meh. English is the default second language in most of the world, and Westminster-style democracy is on paper the most common system of government.
Of course, some of those democracies always return 95% of the vote for the ruling party, so it’s questionable whether they’re actually democratic.
He’s the OP, so I guess he gets to lay down the ground rules. At least he didn’t specify a state religion.