Melbourne and Sydney aren't as boring as Perth. If you don't mind the high taxes they are very nice places to live (I'm from Melbourne, currently living in Singapore).
For racism, Melbourne is probably the best place. Racism is mostly among the older generation and out in the country, as us city dwellers have grown up with many different races around us. Greek, Italian, Vietnamese, Chinese and Indians are everywhere. To me they just seem normal (I'm 28).
Sydney I'm a bit wary of.. I stayed there 2 weeks and nearly got beaten up by an aborigine, as well as seeing a car weaving around the road, crashing into parked cars. I feel that sydney has more racial tension than melbourne (totally subjective).