Even when more than one airport exists in the vicinity, a person would still likely refer to "the airport", not "an airport". Granted that the statement is unclear and might require further explanation, it is the way people speak. In the same vein, I might refer to "the hospital", even when there are several nearby. "He was involved in an accident and taken to the hospital".

If there are many airports in a city, then you could refer to the one you need by its proper name. "Excuse me, can you tell me how to get to the Hoover International Airport?" or something along those lines would easily get the point across. That being said, many places only have one airport. In this case, it is, of course, perfectly fine to just say "the airport". _______________ In response to your recent additions, asking for "the nearest airport" or "an airport" are also fine. That being said, if you need to go somewhere specific (which is likely the case if there are several airports nearby), you obviously shouldn't ask for either of those things. You don't want to end up at the wrong airport, after all!

You are correct that we use "the airport" when there is only one airport nearby. If there are more than one airport in a city (e.g., Los Angeles has several) then you should specify (e.g., LAX or Burbank Airport). However, you would not ask someone how to get to "an airport," since that is too vague. That's like asking how to get to "a restaurant."

If you use "an airport", it means any possible airport - ie. any one will do. This is strange because going to an airport involves either travelling (=specific arrangements) or meeting a traveller (=specific arrangements). If an airport is your destination, you'd certainly know which one! Apart from that, I agree with Brad and Bad... specify the name of the airport.