Westchester is directly north of The Bronx. If you continue
heading north in The Bronx, you will end up in Westchester.
The Bronx is one of the five boroughs of New York City
(Manhattan, Brooklyn, Queens, The Bronx and Staten Island).
Westchester County is part of New York State, but NOT part of New
York City.
Westchester is upstate of New York City, but it is still very
close to the southern tip of New York State. Nobody besides New
York City residents would ever call Westchester "upstate."