You can check with the New Jersey Motor Vehicle Commission (MVC) to find out if you can travel outside of the state with your provisional license. Likely you can since driving out of state is not listed as a restriction for the NJ provisional license, the middle step of the NJ graduated license (GDL) program.
If you are allowed to drive out of state with your New Jersey provisional license you will most likely be mandated by the NJ MVC to abide by the restrictions that NJ places on this type of license. According to the MVC you must observe the following requirements and restrictions while driving with a provisional license:
- No driving between 12:01 a.m. and 5 a.m.
- Passengers must be from your household. Only one additional person from outside your household is allowed in the vehicle
- You can't use cell phones, hand held video games or any other hand held electronic device
- Seat belts must be worn at all times
As for driving in New York, the NYS DMV notes that NYS restricts driving privileges if you are under the age of 18 and have an out of state driver license, or you are any age and have an out of state learner permit. The NYS DMV goes on to state that you must obey the restrictions of both your home state and the NYS restrictions for learner permits or junior licenses while in New York State.
This NYS DMV brochure on for New Drivers outlines what restrictions and conditions are placed on those with learner permits and junior (provisional) licenses that drive within the state of New York.