What happens to the altitude of polaris as you move due west from mamaroneck to chicago?

Polaris moves along with normal altitude a as it is located right above the axial pole north - so, 90ºN. The latitude of Mamaroneck and Chicago doesn't vary by much so it can be considered ignorable.
Altitude wise, we know that Chicago is at about 181m of altitude, while Mamaroneck is at 0m of altitude. Thus, Chicago being in a higher point, Polaris is at a smaller altitude then in Mamaroneck.
As we move west from Mamaroneck to Chicago, the altitude of Polaris decreases.