'Where is the airport?' is a sentence because it contains a complete subject and predicate. It may be a bit confusing at first, but if you're ever confused about the grammar in a question, just switch around the order of the words so that the subject comes first.
Where is the airport?
In this sentence, 'airport' is the subject and 'is' is the verb. However, since the subject usually comes before the verb, you might want to switch them around to make it a bit less confusing.
The airport is where?
Now it becomes more obvious that there is a subject and a verb, and that they form a complete sentence.
Hope this helps!
