Australian Open - Grand Slam tennis tournament. Only in Paris, New York, London and Melbourne!
Melbourne Cup Carnival - a globally recognised and esteemed horse racing carnival.
An entire code of football is centered around this city, AFL. And not only that, the code's professional league has the 4th highest average regular season attendance of any sporting league in the world. Most matches are fixtured in Melbourne.
Olympic Games 1956
F1 - we have a race, only about 20 global cities can boast this,
Melbourne's sporting precinct (includes the MCG - few stadiums have as much history as this, only Berlin's Olympiastadion the Maracana, and probably a few more might contend with it), a precinct still growing.
We've very recently hosted a World Swimming Championships, a World Gymnastics Championships and next year host the Cycling World Championships.
We're probably gonna host the World Cup Final in 2022.