On the subway map
http://www.mta.nyc.ny.us/nyct/maps/submap.htm
your hotel is right near where it says 51 st on the right side on the green line. If you put your cursor on the 51 st. black dot it will say the trains that stop there (E,V,6). The 4 only stops there late at night. Get on the 6 train heading downtown (it may say Lexington ave. local and maybe Brooklyn Bridge on the front of the train). Go one stop to Grand Central and change trains for the 4 or 5 (Express) to Bowling Green (last stop in Manhattan-make sure to get off otherwise you'll be in Brooklyn). OR, as someone above said, walk to Grand Central at 42 st. & Lexington and take the 4 or 5 from there and avoid changing trains.