I flew into NYC with a semi-auto shotgun (and 4-5 boxes of ammo) about 6 years ago for a duck hunt on Long Island, NY with a client. I had zero issues at the airport or driving from the airport in a rental car. It was all locked in a hard case. NYC wasn't exactly the backdrop of the hunt, but it wasn't very far away by my standards.
I've flown to Providence, RI with a bolt action rifle (no ammo) and never had any problems there either. I got a rental car and I kept it locked in a hard case at all times during transport. I traveled into Massachusetts and delivered the rifle to a FFL dealer. I remember him talking about the strange laws they have there, and I told myself to stay far away from MA with a gun after hearing him talk. I wouldn't let that change my traveling through the state plans, but I wouldn't purposely take a gun there.
I've flown to Burlington, VT with a bolt rifle (lots of ammo). Got a rental car and also never had any problems. Again, it was locked in a hard case in the vehicle and I had no problems.
Those are my only 3 experiences with traveling in New England with firearms, but if it were me, I'd leave it all locked up out of reach. Don't draw attention to yourself and it should be easy and hassle free.