Yes — Melbourne is one of the safest major cities in the world for tourists. It consistently ranks in the top ten of the Economist Intelligence Unit's Global Liveability Index, and violent crime against visitors is rare.
CBD and transport: The city centre is well-lit and heavily foot-trafficked until late. As in any large city, be aware of your surroundings around major transport hubs (Flinders Street Station, Southern Cross Station) late at night, particularly on weekends. Keep valuables out of sight on trams and trains.
Neighbourhoods: Virtually all tourist areas — the CBD, Fitzroy, Collingwood, South Yarra, St Kilda, Carlton, Richmond — are safe to walk at night. Areas to be mildly cautious of after dark include stretches of Swanston Street late on Friday and Saturday nights.
Road safety: Drive on the left. Melbourne's tram network means you must stop behind trams when passengers board and alight (the 'safety zone' rule). Speed cameras and red-light cameras are widespread.
Nature and sun: UV levels are extremely high (often 10+) even on overcast summer days. Slip, slop, slap — use SPF 50+ sunscreen, a hat, and UV-protective clothing. If you swim at ocean beaches, check surf conditions and swim between the red-and-yellow flags.
Emergency number: 000 (police, fire, ambulance).