I agree with a previous post. GeoCaching is great. It gives you a reason to get out. There are caches all over the state, both in rurual areas and in much more urban areas. Here is something else to try. I love everything glass. There is a hot shop for glass blowing right on the Asbury Boardwalk. The name is Hot Sands. Wheaton Arts also does glass blowing and is full of exhibits about American Glass. Wheaton is in Southern Jersey near AC.
I like to take my 5 year old to the Planetarium in Trenton. On saturdays the parking is free, the museum is free (and worth every penny) but the planetarium is new and all HD-digital and offers shows targeted to specific age groups. Its 5 bucks a show so its not exepnsive.
Its right next to the state house and you can take free guided tours on saturdays as well. Its a great way to deepen your understanding of how screwed up NJ really is with regard to politics.
The only thing that is tough is that there are no restaurants in the immediate area that are open on the weekends.... so bring a sandwich if you're going to make a day of it.