Given that there are 1,281 international airports in the world (according to Wikipedia), there must be an airport that is ‘centralmost’ depending upon some definition - maybe it has the smallest sum of distances to all the other international airports. Or maybe it is the airport that is closest to the geometric center (projected to the Earth’s surface) of all the other international airports. Or maybe it has the smallest sum of squares of distances to all other airports. Or maybe you want to weight airports based on the population in their catchment; if we’re evacuating the world to a single location, it might make sense to try to minimize man-miles flown, not just airport-to-airport miles for single flights. Whatever; you may choose your definition. I guess we can assume that magic planes can fly nonstop great-circle routes from airport to airport, and that if an airport can provide flights across one national border it can provide flights across all borders, in order to simplify the problem.
So, does this problem have a known solution(s) based on whatever particular definition(s) you choose for ‘centralmost’? Looking at a map of international airports, I would guess maybe Diori Hamani in Niger, but that’s just a WAG.