Do you know the location of the airport (coordinates)? If so, you could (temporarily) spawn an AI aircraft at that location and get the ground altitude, as suggested here:
Apparently this technique has already been used in FSX days 
Another question: how do you get the destination (and source) airport (I am interested in the ICAO code)? Do you subscribe to the airport list, or is there a way to get source and destination from the flight plan (if defined), in a generic (for all aircraft) way?