Well at least you will be next to New York. Kidding, there are great things to do in Jersey. For the outdoorsy type try the Wet Lands Institute which offers a hike on the Salt Marsh Trail. It's Unique to hike in salt water wetlands. There are a host of other hikes but depends wehre in New Jersey you will be, and also access to transportation. Depending on where you come from coastal activities might be the most exciting, such as fishing or boat rentals of which there are many options. Whale watching is also an opetion depending on season. The nightlife of the Jersey shore is a bit of cliche but can also be fun. Of course there is Atlantic City which is one of the few gambling destinations in the US which could be fun to do with your Aunt and Uncle, they have plenty of shows as well.

take a trip to Cape May at the southern tip of New Jersey.
The bay there is just awesome if you're a nature lover. You can camp, hike, fish, cook your fish over your campfire later... I'm from New Jersey and every time I go I have a great time.

Oh, and there's also great bird-watching too if you're into that sort of thing.