What terminal is southwest airlines at jfk at John F. Kennedy International Airport (JFK), Terminal 4 is the base of operations for Southwest Airlines. One of the larger terminals at JFK offers a plethora of attractions and services to passengers. Check the terminal maps and signage for specific gates and amenities if you're traveling Southwest from JFK. A variety of dining establishments, retail stores, and lounges are available at Terminal to improve your journey. Since terminal assignments.