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For a city of nearly 4 million people, Melbourne is remarkably safe. Leaving aside the drunken brawling that's become a feature outside some nightclubs, there's little in the way of serious risk to the average visitor. Street crimes like assaults, robbery and even petty crime like pickpocketing are very rare and even more infrequently directed at tourists.
Be aware that some Melburnians have a rather black sense of humour and will often invent imaginary perils to worry tourists and amuse themselves. Killer UV, enormous snakes, drop bears etc. Take it all with a large grain of salt but of course don't overdo the salt that's bad for your health.
The weather can be changeable, especially in winter and early spring, so bring some warm gear. But, as they say, 'In Melbourne, even the weather is stimulating'. Best seasons are generally considered to be autumn (March to May) and spring (September to November).