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 Newburgh–Beacon 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