When I lived in Maryland, we used to do the same thing at BWI off of Dorsey Road south of the airport. In fact, they even turned it into a small park with paved parking spaces and a little playground for kids. Don't know if it's still there in the wake of 9/11.
Can't do that here in San Antone. Airport security has nothing to do with it, but private security does. Most of the airport is bordered by industrial parks, and it's the private security guards working for these private enterprises who are enforcing trespassing laws rather than anything related to finding a nice spot to watch airplanes land and take off.