Take the Downtown A-C-E (the blue line) from 34th Street-Penn Station to West 4th Street.
Transfer at West 4th Street to the Downtown F train (of the B-D-F-M, the orange line) to 2nd Avenue-Houston Street or Delancey-Essex Street.
Allen Street runs north to south from Houston Street to just below Canal Street. The 2nd Avenue-Houston Street Station will drop you off a couple of blocks west of Allen Street. The Delancey-Essex Street Station is three blocks east of Allen Street, and three blocks below Houston Street.
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 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.
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.
Take the Uptown 1 train (of the 1-2-3, the red line) from 34th Street-Penn Station to 66th Street-Lincoln Center (at Broadway).
You don't have to take the subway; it's 2 blocks. Penn Station is at 34th Street between 8th and 7th Avenues, and 520 8th Avenue is between 36th and 37th Streets.