If you made it Australia and left without going to Melbourne you missed out on a great deal of culture and class (Yes, Australians have that too) Sydney may be the international icon but Melbourne is where everything takes places from Comedy Gala (Australia's answer to Montreal) to the Melbourne Cup (a public holiday there) to an amazing array of Art Galleries, Museums, Gardens, Parks and nearly all sporting events (bar Olympics) takes place there.
Tourism Victoria has amazing websites up with walks around the city. It guides to unknown corners where you see brilliant graffiti and discover the best cafes. It gives historical insights and Melbourne is a planned city so, unlike Sydney) the city forms a grid pattern and no one (I mean it) can ever get lost. There are trams all over the city and again unlike Sydney a ticket covers you for a day's travel not just a destination (just don't forget to validate it). The people, like Australians everywhere, are really nice and friendly and will take their time out to help you. The food is BRILLIANT. If you are a chocoholic you have to try the Chocolate Box.
Melbourne's airports get a little confusing and Avalon appears to be quite in the middle of no-where (you are right, it is nowhere near the city) but there are frequent airport shuttles into the city and to country-side Victoria. The train stations have lockers you can hires for days on end in case you get to the city and feel the need to start exploring. Melbourne is Australia's charity capital too so all head-offices for Amnesty, World Vision, Asylum seekers, Child wise, AYAD exists there so if you in that industry do head down - they are inspiring talks going on all the time.
Try it factor: 5/5 - I go nearly every year because its a perfect harmony of culture, class, food and fun