New York assigns an estate to a county by where the person lived at death — not by where the property sits. A Brooklyn resident who owned a house upstate is a Kings County matter. A New Jersey resident who owned a Manhattan co-op is not a New York County matter, though the apartment will still require a proceeding here.
That single rule decides which courthouse your executor files in, which clerk's practice applies, and how long the first step takes. Below is the court for each county we appear in, followed by a guide for each area — written around what families there actually own, from co-op shares that are not real property to two-family houses that carry a tenant.