「あなたの家から一番近い空港はどこですか？」って英語でなんて言うの？

You would like to ask someone which airport is the nearest to their home. Any of the above suggestions are perfect for such a scenario.

If you wanted to find out what airport is geographically the closest to a someone's home you can simply ask something along the lines of, "What airport is closest to your house?" or "Which airport is nearest to your home?". Both these questions address the desire to find out which airport is the closest to that person's home.

You can simply ask "what is the closest (or nearest) airport to you?" and this generally implies that you are asking nearest to their home/house.

Formally you can ask "Which airport is nearest (or closest) to your home?

If you may have an idea of the airport you can use the phrase "Is Narita the closest airport to you?" or "Is Narita your closest airport?".

The first question is asking where is the nearest airport as is the second question. The first one is asking where it is should in case you need to collect someone from there. However the second is asking because you would want to travel there yourself. Both have implied subquestions to them.

"Which" is when you want to ask about a specific object or place. "Where you live" is another way to say house or apartment or city. I hope that this helps :)

If you want to find out which airport is closest to somebodies house, you can ask them:
"Which airport is closest to your house?"