Yes, you should be able to drive in New Jersey with a valid Puerto Rico driver's license.
According to the New Jersey Motor Vehicle Commission (MVC) foreign motorists with valid driver licenses from qualifying countries are free to drive personal or rental cars while visiting the United States as a tourist but are advised to carry an International Driving Permit. Since your license is from a US area and not technically a foreign license than it should be valid in NJ as well.
States when speaking of US licenses many times also mean US Territories include American Samoa, Guam, the U.S. Virgin Islands, Puerto Rico, the Federated States of Micronesia, and the Midway Islands.
If your PR license is in Spanish and not English you may want to carry an International Driving Permit (IDP) or attach an English translation to the driver's license prior to your arrival in New Jersey. This way if you are stopped by police they will be able to read the English translation and know you have a valid license from Puerto Rico.
If you stay in New Jersey so that you become a resident of NJ you will need to exchange your driver's license from Puerto Rico for a New Jersey license. According to the NJ MVC when you move to New Jersey, you must transfer your out-of-state license within 60 days of your move or before your current license expires, whichever occurs first.
If you have questions about how long you can drive in New Jersey with your Puerto Rico license or general questions about the validity of your license in NJ while you are visiting there contact the New Jersey MVC directly.