This sports centre is called the Melbourne Cricket Ground, but I recommend heading along for some football. Specifically, if you're visiting between about April and October, go and see some Aussie Rules (or AFL) football. AFL is the sport of Australia, and nowhere is it more popular than in Melbourne.
Even if you're not much of a sports fan, this is one exciting game. The playing field is massive, the players are all giants, and sometimes from the heights they leap to you'd think they had wings! Everyone's got a team they support, and every club has its history and its stories. This is the stuff of legends.
Make sure you go with a local - there are a few rules that can be hard to understand without someone explaining them, but you'll get it soon enough!