Buried within* the non-real-time GTFS files the MTA provides shape arrays for each line. The arrays have thousands of Latitude/Longitude points that describe the physical tracks.

* "New York City Transit Subway" link on this page after clicking through TOS.

      {
        "shape_id": "G..N13R",
        "shape_pt_lat": "40.744766",
        "shape_pt_lon": "-73.948280",
        "shape_pt_sequence": "515",
        "shape_dist_traveled": ""
      },
      {
        "shape_id": "G..N13R",
        "shape_pt_lat": "40.744817",
        "shape_pt_lon": "-73.948164",
        "shape_pt_sequence": "516",
        "shape_dist_traveled": ""
      },
      {
        "shape_id": "G..N13R",
        "shape_pt_lat": "40.744866",
        "shape_pt_lon": "-73.948049",
        "shape_pt_sequence": "517",
        "shape_dist_traveled": ""
      },
      
      

These can be used to draw the line on the map.