Well... this has turned into quite the Aussie-bashfest. I am a New Zealander and I did a summer research studentship at ANU in Canberra. ANU is the highest ranked Uni in Australia and I had an excellent time there. I was staying in a hostel with people from all over the world, and never did I encounter any racism. Even on Australia Day (the day that a lot of redneck aussies come out to play), it was very relaxed. I was friends with people of many different nationalities and racism was never an issue, as far as I am aware.
Of course, there are racist people everywhere, and if you are part of a minority group you are bound to come across the odd evolutionary throwback who treats you like crap. But I would say that there are many, many sensible and accepting people who will make up for the horrid ones.
Perhaps you could think about participating in a summer program or just visit the university you are interested in to see what it is like. I would definitely recommend ANU, it was a really good Uni. And although Canberra takes a while to get used to, it's actually a nice city with a great atmosphere.