Melbourne has been listed as the World's Most Liveable City on a number of occasions (there's some kind of International jury process that ranks cities). It's easy to get around using trams or trains (depending where you want to go) and there are things to experience or see both close to the GP venue or farther out.
This
Lonely Planet page may help but there are many other guides online from tourism Victoria and the like.
I've known international visiting friends to find the experience of visiting the Melbourne Cricket Ground and the Sports Museum there to be really special. Melbourne is something of a "foodie" city and there are laneways in the CBD choc full of cool and quality cafes etc.
Being a multicultural city, you can stay in Melbourne but experience the cuisine of different countries by going to different areas of the city - Italy, Vietnam, Greece, China, Lebanon and a range of other countries are concentrated in areas of the city - worth doing some Google searching and away you go!