Immediate family members, i.e., a spouse and/or unmarried children under 21, may apply for J-2 visas to accompany exchange visitors to the U.S. No other family members are eligible for J-2 status. Each person in J-2 status must have his or her own DS-2019. If you have dependents and would like them to join you at some point during your stay at NYU, notify your department of this when you are asked for information for your visa application.
Once in the U.S., individuals in J-2 status are permitted to apply for work authorization from the U.S. Citizenship and Immigration Services (USCIS).
If your dependent has no plans to work and no intention of staying longer than three months, the B-2 (tourist) visa or the Visa Waiver Program is a fine option for visiting you in the U.S.