Estate proceedings, like probate and small estate, are filed in the Surrogate's Court in the county where the Decedent (the person who died) was "domiciled" before they died.
This means the county where the Decedent lived and considered their primary home address before they died. If the Decedent had more than one residence, the domicile is that place where the Decedent intended to return.
A nursing home is not considered a "domicile." In cases where the Decedent lived in a nursing home before they died, file the estate proceeding in the county where they lived before entering the nursing home even if they no longer own or rent the home.