Take the Downtown A-C-E (the blue line) from 34th Street-Penn Station to West 4th Street. All three of these trains (the A, the C and the E) stop at West 4th Street, so it doesn't matter which one you take. The A is an express train, though, so it's only two stops: 34th Street-Penn Station ---> 14th Street ---> West 4th Street. The Cand E are local trains, but there's only one more stop than the A from 34th Street-Penn Station to West 4th: 34th-Penn Station ---> 23rd ---> 14th ---> West 4th.
At West 4th Street, transfer to the Downtown F train (of the B-D-F-M, the orange line). You can take the Downtown F train to 2nd Avenue (at Houston Street) or Delancey Street (at Essex Street). Both of these stops are smack in the middle of the Lower East Side.
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.
No. You would have to transfer at another station that has access to it.
No, but it does stop at penn station and you can take the subway
Take the Uptown E train (of the A-C-E, the blue line) from 34th Street-Penn Station to Court Square.
Park Avenue is about half a mile east of Penn Station.
MetroNorth from Poughkeepsie goes to Grand Central. Amtrak from Poughkeepsie goes to Penn STation. It's very easy to take MetroNOrth to Grand Central and then get the subway to Penn Station.
Take the Uptown E train (of the A-C-E, the blue line) from 34th Street-Penn Station to 53rd Street-5th Avenue. Fifth Avenue is one block west of Madison Avenue.
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.
E-train north.
The 1, 2, and 3 trains go from Times Square to Penn Station. The A, C, and E trains run parallel, going from Port Authority to Penn Station. However, the Port Authority Station and the Times Square Station are connected underground.
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.
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.