Learn Spanish (Latin America): El aeropuerto está en el este.

You would ask, "¿Dónde está el aeropuerto?" You use dónde (where) because you are asking for a static location. If you were asking where a flight is going, you would use adónde (to where) instead.

Why does this sentence use está instead of es?

We use está (from the verb estar) because it describes the physical location of the airport. We always use estar to talk about where things are located, even if that location is permanent.

Doesn't the word este usually mean "this"?

It does! Este often means "this" (like in este boleto for "this ticket"), but it is also the noun for the compass direction "east." You can tell it means "east" here because it is paired with el (the) to make el este.

Do compass directions always need el in front of them?

Yes, when talking about being located in a specific direction, Spanish uses el before the direction word. So you say en el este (in the east), en el sur (in the south), and so on.