Within walking distance to the east of the station is the "Ironbound" district of Newark that has Brazilian bars and steakhouses.. You could do a search on Yelp for the recommended places. Otherwise, not a whole lot to offer in the area.
To get into Manhattan you could either take a New Jersey Transit train (about 20 minutes), or take the PATH train.
Website for the PATH:
http://www.panynj.gov/path/full-schedules.html
Website for NJT:
http://www.njtransit.com/sf/sf_servl...Action=TrainTo
The train will take you to New York Penn Station, and from there it's about a 15 minute walk to Times Square.
If you take the PATH and want to go to Times Square, go to the last stop (33rd St.) and also expect a 15 minute walk.
The Empire State Building is very close to New York Penn Station. If you want to go to Ground Zero, the best bet is to use the PATH, which will take you there directly (via the World Trade Center stop).