Don't stop or do any sightseeing in Mass. A Massachusetts LTC is required to possess a firearm in this state. If you don't have one, you will be in violation of state law. Massachusetts does not recognize any out-of-state permits or licenses.
New York also does not recognize any out-of-state permits or licenses, and they do not issue licenses to non-residents. Don't stop or do any sightseeing there either. And don't get pulled over; NY only recognizes FOPA (Federal Firearms Owner Protection Act) as a defense in court AFTER you've been arrested.
No permit is required to posess or own a firearm in Maine. While traveling, it is recommended to have the handgun unloaded and in a locked container other than the center console or glove compartment of your vehicle.
I strongly recommend you consult the laws of each state in which you intend to travel, whether you're stopping or not. Make extensive notes.
If you break down or have some other kind of forced stop in a jurisdiction where possession of a firearm would get you in trouble - be sure to know your rights:
1) You have the right to remain silent. Use it. Do not inform authorities that you are in possession of a firearm.
2) It is a violation of your civil rights if authorities search your vehicle without either a) a warrant, b) probable cause, or c) your consent. DO NOT GIVE YOUR CONSENT. It is also a violation of your civil rights if police use your non-consent as probable cause for a search.
Know your Federal and State laws. Know your rights. And keep out of trouble. Then you should be fine. Here are some links to get you started, but if it gets confusing, you may want to consult an attorney knowledgeable about firearms laws:
Concealed Carry Permit Reciprocity Maps
NRA-ILA | Gun Laws