You can take the Downtown 1 or 2 (of the 1-2-3, the red line) from 34th Street-Penn Station to Canal Street (at Varick Street).
You can also take the Downtown A-C-E (the blue line) from 34th Street-Penn Station to Canal Street (at 6th Avenue, only one block east of the Canal Street Station on the 1 and 2trains).
Or, you can take the Uptown 1-2-3 one stop, from 34th Street-Penn Station to 42nd Street-Times Square, and then transfer at Times Square to the Downtown N, R or Qtrains (of the N-R-Q-W, the yellow line) to Canal Street (at Broadway, a few blocks east of the Canal Street Station on the A-C-E).
The 6 train (of the 4-5-6, the dark green line) also stops at Canal Street, but you'd have to make two transfers to get to it from Penn Station, and the Canal Street Station on the 6 train is actually connected to the Canal Street Station on the N, R and Q trains. So you might as well just take the N, R or Q.
Take the Uptown 1-2-3 (the red line), one stop, from 34th Street-Penn Station to 42nd Street-Times Square.
Transfer at the Times Square Station to the Downtown N-R-Q (the yellow line) to 14th Street-Union Square.
Take the Downtown 1 local train (of the 1-2-3, the red line) from 34th Street-Penn Station to Houston Street (at Varick Street).
Depending on which exit you use, you might exit the subway on Varick Street between Houston Street and King Street (the next street down). Walk down to King Street, turn right, and walk 1 block east on King Street to Hudson Street. Turn left, and walk roughly 1/2 a block down to 350 Hudson Street, between King and Charlton Streets.
Ninja NY is at 25 Hudson Street, between Reade and Duane Streets. Take the Downtown 2 or 3 express trains (of the 1-2-3, the red line), 2 stops, from 34th Street-Penn Station to Chambers Street.You will exit the subway at the 3-way intersection of Chambers Street, West Broadway, and Hudson Street. Walk 1.5 blocks north on Hudson Street (north is the only direction you can go, since Hudson Street begins/ends here) to 25 Hudson Street between Reade and Duane Streets.
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).