Home Postcodes by state NSW 2784 Postcode 2784 2784 is the postcode for Bullaburra, NSW. Localities with postcode 2784BullaburraNSW Postcode 2784 State or territory New South Wales (NSW) Localities 1 Council area Blue Mountains Council area based on Australian Bureau of Statistics data (ASGS Edition 3), CC BY 4.0. Postcode 2783 · Postcode 2785