here's how I would do it:
when you get off the train at Penn Station, walk downstairs from the Amtrack level to the Long Island Railroad level. walk to the 8th avenue side of the station and board the "E" train to the World trade Center (yes, the train still says it goes to the trade center.) the subway ride should take about 15 minutes. get off at the last stop, walk all the way to the front of the train to exit the subway. you will be on the corner of Vesey and Church Streets, right at the northeast corner of Ground Zero. there actually isn't much to see there, but it can be overwhelming, so you may want to leave yourself time to absorb the emotional aspects of the site.
I'd also give myself a few minutes to walk down to Battery Park. go to the southeast corner of Ground Zero -- Church and Liberty. walk east on Liberty one block east to Broadway. turn right and walk south on Broadway until you get to the park. there are two things worht mentioning here. at the entrance to the park is the Sphere -- it was a sculpture on the plaza of the trade center, and is now a memorial to the trade center. and if you walk acorss the park to the harbor, you can see the Statue of Liberty and Ellis Island in the distance. a trip to the Statue is an all-day event, but you can see it from shore.
at the entrance to the park is Bowling green Station, where you can catch the number 4 or number 5 trains uptown. take the train 3 stops to Brooklyn Bridge-City Hall, then change for the number 6, which is a local. take the number 6 to Park Avenue and 33rd Street. when you get out of the subway, walk up to 34th street and then walk west to 5th avenue. that's where you'll find the Empire State Building. you can take as much time as you want exploring the observation decks. there's also some sort of movie ride, I haven't been on it.
Times Square is located at 42nd Street and 7th avenue -- where Broadway and 7th cross. I'd walk from 34th street. there's a lot of shopping in the area -- the Virgin Megastore, lots of theater stuff, the huge Toys R Us. I like the Hershey candy store on 49th. and there are some nice places to eat -- like John's pizza on 44th and 8th, Ollie's Noodle shop, Carmine's Italian. and if you have time, go to Madame tussaud's on 42nd street -- great wax museum.
to get back to Penn, you can either walk to 34th St. or take the number 1,2 or 3 from Times Square to Penn Station.