The obvious choice is Liberty National Golf Course. It is near the airport and the views of Manhattan are spectacular. While you are in the area try to catch the Broadway show The Book of Mormon, it is the story of America's Prophet with a hilarious look into our history.
Book of Mormon is the funniest play I've ever seen!!! I've now seen it twice and and it was as, or more, sidesplittingly funny the second time as the first!! I am thinking of even taking a good friend for his 50th for my third time. Absolutely the best Broadway show in decades!!
As for golf, what everyone is missing from suggestion (and I'm headed there this am to play) is Plainfield CC, a Ross Gem and most likely NJ's second best course. Yes, it's private, but the head pro, Scott Paris, is a fine gentleman and ambassador of goodwill. I'm sure the "proper" begging letter and a benign choice of timing will land you favorable consideration. Zero harm of trying!
I was at opening night. Never had more fun golfing than I did that night. Turn it off are words to live by.