(From one engineer to another)

Some ways (but neither is entirely free):

1. OAG (Official Airline Guide) - it shows timetables by destination i.e. if your destination is NYC, you go to the NYC section and then look up your departure airport. So you could figure out the various possible departure airports from looking at the section for the arrival airport.

2. FlightTracker PRO at www.thetrip.com - it lets you see the actual arrival display screens (in real-time) for most major airports. So again you can see what flights are arriving at a given time without needing to know exactly which city the flight originally departed from.

2. FlightTrac