Australia's multicultural hub
While Melbourne is a very safe city for its size, the usual precautions still apply as for any large city, including keeping valuables hidden, and travelling with a friend or companion on the street or a train late at night, if possible. Certain areas which are fine during the day can be unsafe at night if you are alone, including the Collingwood and Footscray areas. However these areas are also heavily patrolled by the Victorian Police Force, so provided you stick to main streets (eg: for Collingwood - Smith Street), you should be fine.
Melbourne's red-light districts include King Street in the CBD and Grey Street, St Kilda, but you're more likely to face drunken revellers and unwelcome approaches from street walkers than any major threat. Melbourne City Council has also recently established all-night "Safe City" taxi ranks with security guards on King Street, outside Flinders Street Station and on Bourke Street.