Take the Downtown A-C-E (the blue line) from 34th Street-Penn Station to West 4th Street in Manhattan.
Transfer at West 4th Street to the Downtown D train (of the B-D-F-M, the orange line) to 36th Street (at 4th Avenue) in Brooklyn.
Walk 3 blocks NORTH on 4th Avenue to 33rd Street (streets run in opposite order here: they descend going north, and ascend going south). Make a left onto 33rd Street, and walk 1/2 a block west on 33rd Street to the BPM Hotel, at 139 33rd Street, between 4th Avenue and the Gowanus Expressway.
Take the subway to 34th St (Manhattan). That's Penn Station. Take Amtrak.
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
The Affinia Manhattan Hotel is one block away from Penn Station, you should walk through W 31 St
Atlantic Terminal in downtown Brooklyn. The Atlantic Terminal on the corner of Flatbush and Atlantic connects the Long Island Railroad (LIRR) with most of the Brooklyn and Manahattan subway lines. Grand Central and Penn Station in Manhattan have more tourists, but Atlantic Terminal in Brooklyn has more locals.
Take the Uptown E train (of the A-C-E, the blue line) from 34th Street-Penn Station to Court Square.
The LIRR (Long Island Railroad) stops at Freeport. It would be a shorter trip if you could board the train at the Hunterspoint Station in Queens, but I guess the LIRR does not run from Hunterspoint to Freeport, because when I entered it into the schedule finder, it said that, "This station combination is invalid." So I guess you have to start out from Penn Station. For subway directions to Penn Station, please ask another question, i.e., "How do you get from [insert address here] in Brooklyn to Penn Station?" See the Related Link below for schedules and fares for the LIRR.
About a mile and a half.
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.
approximately $25.00
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.