Asia. That's where more than half the population is.
Between China and India alone, that's like 40%. When all the other nations are factored in, it's closer to 60%.
For full fairness, Earth capitol should be somewhere between the two. Let's build it in the Himalayas. We can just tunnel under all the mountains and build a massive underground city complex. For full shits and giggles, we can call it Agartha.
Alternative options - build a massive base on the moon that is technically the possession of all nations and no nation simultaneously. Or somewhere in Antarctica. Or as a massive oil-rig style sea platform in the Pacific Ocean as an autonomous entity.
Most of those options are physically infeasible (we don't have the technology or materials to safely and effectively build in extreme conditions), but since the entire concept of humans ever actually agreeing to it under current social conditions, the whole thing is fantasy anyway, so might as well run with it.
adjl posted...
If the earth tried to become one nation, fighting over where the capital should be would fragment it again.
People complain about the UN being in New York all the time.
Ironically, a significant number of people complaining are actual New Yorkers who wish it would go somewhere else.