It depends of the airport.
Some airports are very small and have no buildings.

But if you are talking about big airports, then there are two main causes:
- your game hasn't finished loading the scenery yet. Stop moving (hit PAUSE) and wait some second there to check if the scenery continues loading (more and more buildings appear, textures get more precise, terrain elevation as well, etc...)
- airport buildings are not autogen, maybe your "Scenery Complexity" slider is set too low, try pushing it to the right.