Yes, Penn Station is close to Grand Central Station. They are less than a mile apart But, if you are asking because you are planning on walking or taking a bus or taxi from one to the other...don't. You can just take the subway: take the Uptown 1-2-3 (the red line) one stop, from 34th Street-Penn Station to Times Square.
Then transfer at Times Square to the S shuttle train (color code grey) east across 42nd Street, from Times Square (West 42nd) to Grand Central (East 42nd) You can also take the Uptown A-C-E from Penn Station to Times Square, but this will require you to walk through a long, hot, smelly underground tunnel. Since the Times Square Station is at 7th Avenue, while the A-C-E line runs up and down 8th Avenue, the A-C-E does not stop at Times Square. It stops at 42nd Street-Port Authority Bus Terminal.
The underground tunnel connects the Times Square Station to the A-C-E line, so you can transfer without exiting the subway system So, it is preferable to take the 1-2-3 from Penn Station to Times Square, so you won't have to walk through the tunnel. But if you can't find the 1-2-3 or something (or if the A-C-E just happens to be right there when you get off your train) you CAN take it to Times Square.
Grand Central Station at night. The Main Concourse at Grand Central Station as usual is filled with crowds of people rushing to trains or subways. * Grand Central Station street and mailing address.
Google Map - Map already has street address. Mapquest - Copy street address into search box.
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