I agree with S. Ranck that most likely there would not be a single capital where the entire government is located. However, in terms of a city that serves as a figurehead for the “world government”, it would very likely be New York City.
New York is already where the United Nations has their official headquarters, and that’s the closest thing we have to a “world government”. It has already been described by many as the world’s cultural and financial capital.  It is the largest and most influential city in the world’s most powerful country.
From a practical standpoint, London and Singapore would function as the administrative centers for Euro-Africa and Asia-Pacific, respectively.
One could also make a good argument for Geneva, on the grounds that many international organizations are headquartered or otherwise located there, and Switzerland is universally respected as a neutral place where all parties can sit down and have a round table discussion. So perhaps Geneva would be a figurehead or legislative capital, with New York, London and Singapore as the primary executive centers.