Jawaban:

Either “at” or “from” could be correct, depending on the context. If someone called and asked if you could pick them up, and you asked where, they’d say “at the airport” (location).

However, in another situation, you might have someone call you and ask, “Could you pick me up from the airport and take me to the hotel?” (So you’d have a “from…to” kind of statement).

But generally, most people (including most editors) wouldn’t complain if you used either “at” or “from” unless it would noticeably change the meaning of the sentence.

Especially in writing dialogue, you can get away with these different shades of meaning, since people generally speak casually; only in very formal writing or for a very specific context would you need to worry about something like this.