MacQuarie Point and the Royal Botanic Gardens are north-northeast of St. Mary's Cathedral. I'm on the east side of MacQuarie Point, not far from Mrs. MacQuarie's Chair (33°51′38.61″S, 151°13′20.90″E) (Google Maps).
According to the Australian National Botanic Garden website, there are 76 Banksia species, and all but one occur naturally only in Australia. This is one of the iconic Australian wildflowers, along with Golden Wattle, Waratah, and others.