The 179th Street station (F train) at Hillside Avenue can claim to be the easternmost subway, as in underground, station in the city (though the Far Rockaway station (A/H) is further east, it was originally built for the Long Island Rail Road).
179th Street also can make the claim of being the final station in the original IND run, as it was added to the end of the 6th Avenue/Queens Blvd./Hillside Avenue line in December 1950, 13 years after its neighboring 169th Street station. Original IND construction began in the late 1920s.
Ironically the 169th and 179th Street stations are the only two stations I have never been in. I had my chance this day in August 2012, but passed.