Question

During the month of January, at which location in New York State is the Sun lowest in the sky at solar noon?

Answer 1

That would have to be the northern-most point in the state.
The northernmost part of New York State is a line that runs
about 68 miles along the 45th parallel of north latitude, roughly
from Rooseveltown to Rouses Point.  Anywhere along that line
sees the sun at the same altitude at local solar noon.