I dont live on melbourne but have had a few short visits in recent years & these are a few of the things that we enjoyed.
MCG tour - loved it could've spent the day.
Melbourne Museum
Great ocean road day trip (do the helicopter flight)
Swmbo went to Phillip island to see penguins
Melbourne zoo
And any on the gazillion eating precincts throughout the city.
Art gallery
The big arse church on the corner (St James i think ? ? ? ) in the city
Casino
?
St kilda beach
Really like melbourne lots to see & do but the crowds of people do get to me after a while
I'm sure the local will offer better info but these are some of the things we enjoyed as visitors
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