Overlandsailor, well, I just got back from South Jersey, Stone Harbor to be exact, but since you're not going that far south, you have to check out Point Pleasant in Central Jersey, there's a great little boardwalk for the kids. And if you want a learning experience, go to Princeton, and if you do, you have to go to the center of town to check out The Street on Princeton U. campus. The Street is full of great restaraunts and is an overall great experience for everyone. Also, you've gotta have ice cream at Thomas Sweets [in Princeton]...it might well be the greatest ice cream on the face of the Earth. Also DreamPiper hit the nail on the head with Liberty State Park/Liberty Science Center in scenic Jersey City. Have I mentioned that the Statue of Liberty is in New Jersey? That's all I can think of off the top of my head, hope you have fun.
On edit:
And if you're looking for food here are some suggestions:
Northern Jersey: Rita and Joes, Jersey City New Jersey, right on the corner of Broadway and Wallis Ave., great Italian food, and I would know.
Puccini's [spelling]: Also in JC, on broadway, just down the road a piece from Rita and Joes, more great Italian food.
Central Jersey: Anything on The Street, Princeton University Campus, Palmer Square.
CP