Melbourne:-
1)Great Ocean Drive
2)Penguin Island
3)MCG
4)Crowne Casino
5)Walk on the Flinders/Collins Street and shopping of expensive brands
6)For shopping at a reasonable price u can check out DFO (Duty Free Outlet) near Crowne Casino.
7)Sea Life Aquarium - if you have time
8)Melbourne Zoo - if needed
9)Parliament House Sydney
1)Sydney Harbour Bridge
2)Opera House
3)Darling Harbour
4)Bondi Beach
5)Sea Life Sydney
6)You can also do a day tour from Sydney to Canberra Brisbane
1)Story Bridge
2)South Bank,Queensland
3)Queen Street Mall
Most important places in Sydney I would suggest :
. Harbour Bridge . Darling Harbour . Ferry . Harbour Bridge climb . Bondi Beach . Cornulla Beach . Blue mountains . Three sisters . Sea life aquarium and wildlife . Sydney Tower . Star city Casino