From the fact that the Lian Yu is somewhere in the Pacific, we can assume that the Queen's Gambit left from the west coast of the United States.
While it is never specified, it is heavily implied that the port the Gambit left was in or very near Starling City, as Sara was shown to have been visiting home the night before the trip, and went on the trip in secret.
In City of Blood (S02E21), Felicity mentions that she moved 1000 miles from Las Vegas, presumably to go to school in Starling City.
Where is the fictional Starling City located?