Yes. Take the Downtown 1-2-3 (the red line), 1 stop, from 42nd Street-Times Square (at 7th Avenue) to 34th Street-Penn Station.
Penn Station is closer. Penn Station is less than half a mile south of Times Square, while Grand Central is a little over a mile east of Times Square.
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.
No, it leaves from Grand Central Terminal. The Scarsdale station is a Metro-North station, on the Harlem line. The terminus for Metro-North trains is Grand Central, not Penn Station.
No, the N train (of the N-R-Q-W, the yellow line) does not stop at Penn Station. But it stops at Times Square. Take the Uptown 1 train (of the 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 N.
Take the Uptown 1-2-3 (the red line) one stop, from 34th Street-Penn Station to 42nd Street-Times Square. Transfer at Times Square to the R train.
Take the Uptown 1-2-3 (the red line), 1 stop, from 34th Street-Penn Station to 42nd Street-Times Square. Transfer at Times Square to the R.
Grand Central because you can get Metro-North trains, which run on a schedule and are cheaper than Amtrak. At Penn Station, you can get Amtrak, which runs less frequently, and is more expensive. Amtrak stops only at Penn Station and Metro-North only stops at Grand Central
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 1-2-3 (the red line) from 34th Street-Penn Station to 42nd Street-Times Square, and transfer there to the N.
Take the 7 train to times square and then take the 1 2 or 3 train downtown 1 stop to Penn Station.
Take the Uptown E train (of the A-C-E, the blue line) from 34th Street-Penn Station to Court Square.
Take either the blue line (the A-C-E) or the red line (the 1-2-3) ONE STOP UPTOWN, from Penn Station (34th Street) to Times Square (42nd Street).At the Times Square Station, transfer to the S shuttle train (color code grey) east across 42nd Street, from Times Square (West 42nd) to Grand Central Station (East 42nd).