I am getting my NJ license in June, but shortly after that i am moving to NY, what am i going to have to do?

Yes wait till you get to NY and establish a residency. To obtain a drivers license in any state you almost always have to "prove" you are a resident of that state. That means you will need an actual address. It sometimes is an effort to prove a valid address. You may be asked for two items to prove the address is valid. The following have been acceptable proofs: 1. A credit card statement mailed to you ar the NY address. 2. A bank statement mailed to you at the address. 3. A rental lease for the address. 4. A telephone statement mailed to the address. 5. Any business correspondence mailed to you at the NY address. 6. Any government document or correspondence mailed to you at the address in NY. As it takes time to establish a residence in any state you will have 90 days to establish the new residency before you must obtain the NY drivers license. If you will be living with your parents it may be easier to wait till they establish their residency and all drivers go together to obtain the new license. If you are about to buy a car wait till you establish the NY residency or else you may have to pay both NJ and NY sales tax on the car.