The easiest way is to take the Downtown 1 train (of the 1-2-3, the red line) from 34th Street (Penn Station) to 23rd Street. It's only two stops. You'll exit on 23rd Street and 7th Avenue, on the west side of the street (the west side of the street is the Downtown side, and the east side is the Uptown side).
You'll need to walk east to go to 23rd between 7th and 6th.
Take the Downtown C or E trains (of the A-C-E, the blue line), one stop, from 34th Street-Penn Station to 23rd Street (at 8th Avenue).
You'll exit on the west side of 8th Avenue (the west side of the avenue is the Downtown side, and the east side is the Uptown side). The address 333 West 23rd Street is between 8th and 9th Avenues, so walk half a block west on 23rd Street to number 333.
Take the Downtown C or E trains (of the A-C-E, the blue line) or the A late nights, 1 stop, from 34th Street-Penn Station to 23rd Street (at 8th Avenue). Then walk 4 blocks west to 12th Avenue.
Take the Uptown 1-2-3 (the red line), 1 stop, from 34th Street-Penn Station to 42nd Street-Times Square.
Transfer at 42nd Street-Times Square to the Downtown N or R trains (of the N-R-Q, the yellow line), 3 stops, to 23rd Street (at Broadway). Then walk 4 blocks east on 23rd Street to 3rd Avenue: Broadway ---> Madison Avenue ---> Park Avenue South ---> Lexington Avenue ---> 3rd Avenue.
Probably the best way to get there is to take the C or E train from Penn Station to the 23rd street stop or the 1 train to the 28th street stop. However, to be completely honest, you could walk from Penn Station to 208 W 23rd Street in around 10-15 minutes.
No, the AirTrain takes you to and from the subway, and the subway takes you to and from Penn Station. Take the AirTrain to the Howard Beach Station, and get the Manhattan-bound A train (of the A-C-E, the blue line) to 34th Street-Penn Station.
Take the Downtown 2 or 3 trains (of the 1-2-3, the red line) from 34th Street-Penn Station to Wall Street (at William Street).
Yes, the A express train goes from Penn Station to Chambers Street. It's 4 stops (unless you are traveling at night, when the A runs local). The Chambers Street station on the A and C trains is at Church Street.
Take the Uptown E train (of the A-C-E, the blue line) from 34th Street-Penn Station to Court Square.
You don't need to take the subway to get from Penn Station to 28th Street and 8th Avenue (which is in the Chelsea neighborhood, by the way, not in Greenwich Village or Greenwich Connecticut). Penn Station is at 34th Street between 8th and 7th Avenues. So you can just walk there.
Take the Uptown 1-2-3 (the red line) from 34th Street-Penn Station to 42nd Street-Times Square, and transfer there to the N.
Penn Station is at 34th Street so it is 20 blocks away from 54th St. You would take the subway two stops north.
Take the Uptown E train (of the A-C-E, the blue line) from 34th Street-Penn Station to Lexington Avenue-53rd Street. This station is connected to the 51st Street Station on the 6 train (of the 4-5-6, the dark green line), so you can transfer without exiting the subway system. Transfer to the 6, and take the Downtown 6 to 33rd Street, 28th Street, 23rd Street or 14th Street. All of these stops are on Park Avenue South.
Take the Downtown 1 train (of the 1-2-3, the red line), 1 stop, from 34th Street-Penn Station to 28th Street (at 7th Avenue).
The A train (of the A-C-E, the blue line). Take the Downtown A train from 175th Street to 34th Street-Penn Station. Entrance to the 175th Street station is included inside the bus terminal complex.
Long Island City, Queens is at the edge of the Hudson River. Long Island City is the area that is directly across from about 34th Street to 65th Street in Manhattan.You can take the LIRR (Long Island Railroad). See the first Related Link below. Leave Penn Station as the From Station, and select Long Island City as the To Station.There are also several subway lines you can take:The 7 trainYou can take the 7 train (the purple line) to Vernon Boulevard-Jackson Avenue, Hunter's Point Avenue, Court Square, or Queensboro Plaza.Take the Uptown 1-2-3 (the red line), 1 stop, from 34th Street-Penn Station to 42nd Street-Times Square. Transfer at 42nd Street-Times Square to the 7 train .The E trainYou can take the E train (of the A-C-E, the blue line) directly from 34th Street-Penn Station to Court Square-23rd Street or Queens Plaza.The F trainYou can take the F train (of the B-D-F-M, the orange line) to 21st Street-Queensbridge. Take the Uptown1-2-3, 1 stop, from 34th Street-Penn Station to 42nd Street-Times Square. Transfer at 42nd Street-Times Square to the Downtown N-R-Q (the yellow line), 1 stop, to 34th Street-Herald Square.Transfer at 34th Street-Herald Square to the Uptown F.The N or Q trainsYou can take the N train to Queensboro Plaza. Take the Uptown 1-2-3 (the red line), 1 stop, from 34th Street-Penn Station to 42nd Street-Times Square. Transfer at 42nd Street-Times Square to the Uptown N.Note that Queens Plaza and Queensboro Plaza are two separate stations.See the second Related Link for a complete New York City subway map.