Anywhere with parkland will attract galahs, sulfur-crested cockatoos and rainbow lorikeets without any trouble. I've lived in Melbourne for the best part of this year and even in the Royal Botanic Gardens (a short walk from the city) you could see all sorts of wild birds. Corellas and crimson rosellas are some more common parkland parrots but you won't find them right in the city as often as those other three species.
I have seen quite a few Galah's, Rainbow lorikeets, Western Corella and even a huge flock of Short-billed Black Cockatoos! It is pretty awesome, as the black cockatoos are a true rarity outside Australia.
