The easiest and fastest way to get from EWR into the city is to take the AirTrain from your terminal to NJ Transit. It takes between seven and 11 minutes to get to the AirTrain station from your terminal, depending on the terminal, and about three minutes to get from there to the train platforms. Getting to Penn Station on NJ Transit takes 27 minutes. Another more expensive option is to buy a seat on Amtrak, but those trains come much less frequently.

As for things to do, I recently walked around Little Italy when the weather was nice -- found a small spot called Parm that has an amazing chicken parm. Not super cheap but worth every cent!