From Newark Penn station, you have 2 main options of getting into NYC: NJ Transit train (costs more) or PATH.

NJ Transit train will take you into New York Penn station. I don't recommend this route, unless you want to see the new Moynihan Station, though B&H is worth a visit if you need a camera or other electronics.

PATH takes you to either towards WTC or 33rd streets. WTC route only has one stop in Manhattan, at WTC.

33rd Street route stops in multiple places, starting near Greenwich Village and then along 6th Avenue to 33rd Street (just south of Macys on 34th).

Once you get to Manhattan, Google Maps is your friend. Our public transportation system is called the MTA NYC Transit.

mta.info is the official website for NYC transit, and MyMTA (still has a beta label) is the official App.

All MTA busses and subway take mobile contact-less payments, either from your card, or your phone.

There are various ways to get uptown for Broadway and museums. But on the museums, the art museums are on the east side of Central Park, with the Museum of Natural History on the west side of town. And for WTC, you'd just take the PATH to WTC, which exits into the Occulus.

One word of (personal) caution, I actually don't suggest visiting the islands in Winter after business hours. It's dark af. Otherwise, one actual note of caution. There is only ONE vendor that offers tickets that stop at the Statue of Liberty and Ellis Island (https://www.statueofliberty.org/visit/tickets/). All other tourist companies offer rides AROUND the islands and do not stop there. Make sure you know which one you want. Also, the only one that is open departs from Battery Park at the south end of Manhattan, the one on NJ side is closed until March.

Dumbo is in Brooklyn. If you want to see it, take the PATH to WTC, then A\C (Blue line) to High Street - Brooklyn Bridge. OR the 33rd Street route to 14th Street, then transfer to the Downtown\Brooklyn F train (orange) to York Street in Brooklyn. Not worth visiting while on a business trip, unless you're with a date.

If you plan to go near the water, dress warmer since it will be dark after you leave work, with a stronger breeze. If you don't have a scarf, get one.