Hiking boots is probably the right move. With snow on the ground, they're the least you'll want. If there's ice, you'll probably want some microspikes. Heavier snow means gaters and/or snowshoes.

You might think that driving to NYC is a good idea, but I'd like to disabuse you of that notion. It's a long drive and the traffic will be no fun. Maybe park in Stamford or New Haven (CT) and take the train into NYC and walk around. New Haven has famous pizza, and Stamford has some great restaurants downtown (I used to live and work there).

It'll probably take about 5 hours to get from Conway to lower CT. Maybe spend a day just driving back roads to get down there; it's better than 5 hours of highway driving. If you do take the highway, I'd go over to VT and take 91 south; you'll miss Boston traffic that way.