Home Postcodes by state TAS 7257 Postcode 7257 7257 is the postcode for Cape Barren Island, TAS. Localities with postcode 7257Cape Barren IslandTAS Postcode 7257 State or territory Tasmania (TAS) Localities 1 Council area Flinders Council area based on Australian Bureau of Statistics data (ASGS Edition 3), CC BY 4.0. Postcode 7256 · Postcode 7258