I assume you mean serious kart racing (not kids bumper stuff). If that’s the case, I have names for the 3 most important outdoor tracks in NJ:
1) New Jersey Motorsports Park in Millville, NJ (this is very new)
2) Old Bridge Township Raceway Park, Englishtown, NJ
3) Wall Township Speedway, Wall, NJ (this is an oval with 30% incline banks)
You can find more info on their websites. However, you can also check www.na.motorsports.com/tracks/nj
I would consider the Raceway Park in Englishtown and also the Motorsports Park In Millville.