3 weeks in Jersey?? Sh!t man, if I didnt live here and have a life I'd go nuts!!
But yeah, we have a pretty sweet ass beach thing going on. Atlantic City is fun if you like gambling and scumbags. We have 6 Flags in the Jackson area (central Jersey) and Ocean City, Wildwood, and Cape May in the southeastern side (these are my favorite beach places to go, Wildwood Crest's boardwalk is awesome!)
Depending on transportation, you could easily hit NYC and Philly. South Street in Philly is pretty cool, and there's some fun bars scattered through the city (Finnigan's Wake is a mindfvck but easy sarging grounds). Up in western North Jersey you can do some pretty awesome hikes and outdoor type things.
****Just noticed you're only 17, you wont be able to hit the bars but hey, you can probably sneak into Atlantic City and at least get plastered in the casino bar without getting carded, just dont try to gamble too much.