I was in NYC in 1985 for my high school Senior Class trip. As an 18-yr old, I paid absolutely no attention to where things were in relationship to each other; we just went where we were told to go! So, this may be a silly question to all of you natives out there, but where does Penn Station sit in relationship to Times Square, Broadway, The Empire State Building, the 911 mmemorial, etc? What is within walking distance; i.e. a mile or less? I'm sure I can figure out the subway system, but I may want to do a little walking to sites as well, if it's do-able. I'm not very versed in the geography of the area....
You can split most of the major tourist attractions into those in Midtown and those in the Financial District.
Penn Station is in Midtown, and within a 10 minute walk of Times Square (which is at the intersection of 42nd Street, 7th Avenue, and Broadway), and the Empire State Building. Other sights to see in the area would be Herald Square (with Macy's, which erroneously claims to be the world's biggest department store, directly across the street from Penn Station), Bryant Park, the Museum of Modern Art, the 5th Avenue shopping district, the Morgan Library, Grand Central Terminal, the Chrysler Building, and the United Nations. If you were to walk to all of the places I just listed, it's probably 3 or 4 miles total.
The 911 Memorial is in the Financial District, which is further away -- probably about 45 minutes if you walk, maybe 15 minutes by subway. That area also has the Federal Reserve Bank of New York, the location of the first US Capital, where George Washington was sworn in as president, and is a short walk to the ferry to Ellis Island and the Statue of Liberty.
There is more stuff to see in both areas, and outside those areas (the Metropolitan Museum of Art, for example, is on the Upper East Side) as well.