If you were going to visit NJ the top things I suggest you do or see is:
1. Visit the jersey shore. There are tons of beaches with boardwalks that have games and rides. Seaside, Wildwood, Point Pleasant, Belmare and so much more. I'm not one for the beach but just to walk on the boardwalk and maybe take the kids on the rides can be a fun way to spend your day.
2. Drive or take a train trip to NY City. You could go for the day. There are tons of broadway shows you can see if you like entertainment. If you like to shop you can walk for miles and miles with lots of stores to spend your money at. The restaurants are fantastic. Some are pricey because they could be tourist traps but the food normally is fantastic and memorable. I used to work in the city and I can still remember the lunches I had in the city. Nothing like NJ at all. Try their bagels! Bagels in NY are so much better than NJ.
3. If you like amusement parks then a day at Great Adventure is for you. Okay, it may cost a fortune to get in but if you plan to stay a while in NJ then a season pass is well worth the cost. Not only do you have rides to go on but they have a safari that you can drive though. My kids just love seeing the large animals like Elephants and giraffes that they can't normally see in a regular zoo. Well, maybe not the giraffes. They were so frightened and screamed and cried when they came up to the car. My little girl Naomi still talks about them being so big.
4. From time to time some towns have street fairs. The fairs consist of food, crafts and sometimes there are rides or games for the kids. Last year we attended quite a few with the triplets. At one there was a clown that gave my kids balloons. Another fair had tons of seafood to eat. The towns usually close their streets down. It's a nice way to spend the day. I love looking at all the arts and crafts that are displayed at each booth.
5. If you like to shop there are tons of malls in NJ. Some of them are about 1/2 hour away from each other. There are also tons of shopping outlets. Jackson outlets are really great to get some discounts of clothing especially children's clothing. You can spend the entire day there just shopping and run up your credit cards big time. I try to go there maybe only once a year because it can be very dangerous for your pocketbook.