When I used Google maps to look at the closest border crossing from the centre of Nunavut, it was Maine. I had expected it to be the Alaska Crossing (from Whitehorse) as well, but it was MUCH farther. It's a LONG trip. I even tried to figure out if the St. Pierre and Miquelon crossing was closer but it wasn't obvious to me.
And the closest crossing from Montreal is on the border with New York. I've never driven that route, though (I'm always coming up from New England, so I end up going through VT).