Airports get built "close" in the sense that most international airports are named after a city, and the distance to that city is generally minutes rather than hours of travel.

Airports get built "far away" in the sense that, between land prices and noise abatement, airports are generally on the very outskirts of a city at the time they are built and the city's central train station will be much closer to the city centre.

But apart from military bases on remote islands, no airports are so remote that "don't worry where you ditch the plane if there's a problem, there's nothing near the airport" would be an option :)