According to the New York new driver's brochure, a motorist with a learner's permit, junior permit or junior license may drive outside of New York State if it is allowable by the laws of the other state(s).

If you drive out of New York, you must obey that state's learner or junior permit and license restrictions that may apply. The NYS DMV suggests that you check with the police or motor vehicle authorities of the states which you plan on visiting in your automobile.

The Massachusetts Registry of Motor Vehicles (RMV) notes that you must be at least 16 years of age to drive in Massachusetts, even if you hold a valid driver's license from another state. If you live in MA you must be at least 16 and 1/2 to obtain a Massachusetts driver's license.

The Massachusetts RMV states that teens with out-of-state driver’s licenses can operate a vehicle in MA. The MA Junior Operator’s License (JOL) fact sheet states that passenger and time restrictions do not apply to out of state teenagers. Here it notes the passenger restriction only applies to a person who holds a junior operator’s license issued by the Commonwealth of Massachusetts.

If you have restrictions on your home state’s license, those same restrictions apply while you are operating in MA the JOL fact sheet notes. Furthermore, you may be subject to licensing action by your own state if you operate a motor vehicle in Massachusetts in violation of the terms of your own state’s license laws.

Since the minimum age for MA drivers is 16 1/2 we checked with the Massachusetts DMV to make certain at age 16 you can drive there with your NYS permit. The MA DMV representative we contacted stated that yes, you can drive in Massachusetts at 16 with an out of state permit. You must however follow the rules of your state and the rules of Massachusetts she said.

Since the MA JOL fact sheet noted that the MA time and passenger restrictions do not apply to out of state teen license holders going through a graduated driver's licensing process we would advise you to contact the MA RMV directly to find out what restrictions they want you to adhere to while operating a vehicle in their state with your New York learner's permit. 

So it appears that yes, you can drive in Massachusetts with your New York permit but you should check with both the NYS DMV and the MA RMV to find out for certain what restrictions and conditions you need to follows according to the laws of each state.