As mentioned best way to enter new england would be PA I81 to I78 east then to either the tapenzee Bridge ( I287 to I684 to I84 east or more north and less traffic would be the NewburghโBeacon bridge (I87 north to I84 east)
I would avoid I95 all together... especially through NJ,NY,CT!!
I do remember seeing some rvers bringing dogs to liberty Harbor, I would call in advance about their dog policy or check online. And again as mentioned LH would probably be your best choice for visiting NYC.
BTW, Welcome to the forum!
Mike
2022 F-150 3.5 EcoBoost 4X4 Supercrew GCWR 19,500 157WB
Payload 2476 Maxtow 13,800 3.73 Equalizer 4 Pt Sway Hitch
2017 Jayco Jay Flight 24RBS
Old TV, 07 Toyota Tacoma, Double Cab, Factory Tow Pkg, retired towing at 229K. (Son now owns truck)