Just got back from a trip to Melbourne & Sydney. Here are my recommendations and feedback:
Melbourne: It will be the winter time in the Southern Hemisphere so bring appropriate clothing. It's pretty rainy and cloudy in Melbourne this time of the year. On Wednesday night I recommend going to Queen Victoria Market near Chinatown. It's a fun night market with food vendors and small local shops. They have a silent disco that prances around as well.
On a different night visit the Royal Botanical Gardens for Lightscape. Its the park lit up with music and different art works. If you've been to burning man it's somewhat reminiscent of the light and art work there.
The must do tour is to go to Moonlit Sanctuary. There we got to feed & pet a koala bear, feed kangaroos, wallabees, and ducks. They have different animal talks and is a true Australian experience. From there visit Point Leos a Southern Australian winery and take an hour to walk their Sculpture Garden with art work from both local Australian Artists and some of the most well known artists in the world like KAWS. If you want to venture on to Sanctuary to see a beach town you can (we didn't cause it was rainy, we visited a friend in Chelsea which was also a beach town, and our baby was sleeping)
For food I recommend Cumulus Inc. on Flinders Street, the restaurant at the Park Hyatt, and there's a really impressive diverse mix of people & restaurants throughout Melbourne. The only tour that was recommended that we didn't get to do was the sports stadium. Given that the other recommendations ended up being excellent I assume this too is worthwhile if you have the time.
For Sydney I thought there would be more to do but found it to be average as far as activities and events when we were there. Definitely go visit the Sydney Opera House and see a show there. Shows aren't every day so check and buy in advance. Go to the Shangri-La and have a drink or eat at the restaurnt there with views of the Bridge & Opera house from high above, visit their version of Conney Island at Luna Park, they have an aquarium, museums, and local zoo all in the CBD. Also just walking around the harbor is really nice and you can take the ferry's around to the other side for some nice sightseeing.
Hope this helps for those wanting to explore Australia!