With NY state MM licence, can I purchase in NJ?

No

Google medical marijuana reciprocity for lists of states you can use your card

Closest state that will allow out of state mmp is Massachusetts

Unfortunately no

Not Yet.... There are, however, other states that will accept your NY card. Try a Google search to find out which states, something like: "states that accept New York Medicinal Marijuana Program" (without the quotes). Best of Luck!!