You can take the Uptown B-D-F-M (the orange line) from Broadway-Lafayette Street (at Houston Street) to West 4th Street.
Transfer at West 4th Street to the Uptown A-C-E (the blue line) to 34th Street-Penn Station.
Note that the Broadway-Lafayette Station is technically located at Houston Street between Broadway and Crosby Street, not Broadway and Lafayette Street. Crosby Street runs between Broadway and Lafayette Streets, but the station is called the Broadway-Lafayette Station because both Broadway and Lafayette are major streets, while Crosby is a minor street.
If you are coming from further south on Lafayette Street, then take the Uptown N, R or Q trains (of the N-R-Q-W, the yellow line) from the Canal Street Station (at Centre Street, which is one block east of Lafayette Street) to 42nd Street-Times Square.
Transfer at Times Square to the Downtown 1-2-3 (the red line) one stop to 34th Street-Penn Station.
To get from Penn Station to Worth Street, you can take the 1 subway line. Board the 1 train at 34th Street-Penn Station and travel downtown. Get off at the Chambers Street station, which is close to Worth Street. Alternatively, you could take the A or C train from 34th Street-Penn Station to Chambers Street for a similar route.
You can take the Downtown A-C-E (the blue line) from 34th Street-Penn Station to West 4th Street, then transfer at West 4th to the Downtown B-D-F-M (the orange line) to Broadway-Lafayette Street (at Houston Street).If you are going further south on Lafayette Street (around the City Hall area), then take the Uptown 1-2-3 (the red line) one stop, from 34th Street-Penn Station to 42nd Street-Times Square. Then transfer at Times Square to the Downtown N, R or Q trains (of the N-R-Q-W, the yellow line) to Canal Street (at Centre Street, which is one block east of Lafayette Street).
You can take the Downtown A-C-E (the blue line) from 34th Street-Penn Station to West 4th Street, then transfer at West 4th to the Downtown B-D-F-M (the orange line) to Broadway-Lafayette Street (at Houston Street).If you are going further south on Lafayette Street (around the City Hall area), then take the Uptown 1-2-3 (the red line) one stop, from 34th Street-Penn Station to 42nd Street-Times Square. Then transfer at Times Square to the Downtown N, R or Q trains (of the N-R-Q-W, the yellow line) to Canal Street (at Centre Street, which is one block east of Lafayette 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.
To travel from LaGuardia Airport to Penn Station using the subway, you can take the M60 bus from the airport to the Astoria Blvd subway station. From there, you can transfer to the N or W train and take it to 34th Street-Herald Square station, which is near Penn Station.
To get to the Hayden Planetarium from Penn Station, take the A, C, or E subway line from 34th Street-Penn Station. Transfer at 42nd Street-Port Authority Bus Terminal to the 1 subway line, then travel uptown to 79th Street. From there, it's a short walk to the American Museum of Natural History, where the Hayden Planetarium is located.
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).
To get from Penn Station to 54th Street in New York City, you can take the 1, 2, or 3 subway lines from 34th Street-Penn Station. Transfer at Times Square-42nd Street to the N, Q, R, or W trains heading downtown. Alternatively, you can also walk a few blocks to catch the E train at 34th Street-Penn Station, which will take you directly to 54th Street.
To travel from Penn Station to 851 Grand Concourse in the Bronx, take the 2 subway line from 34th Street-Penn Station station towards Wakefield-241st Street. Transfer at the 149th Street-Grand Concourse station to the 4 or 5 line, and then continue to the 167th Street station. From there, it's a short walk to your destination at 851 Grand Concourse.
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.