The City Circle Tram is a must-do. For one, it gives you a nice overview of Melbourne's top tourist attractions. More importantly, it's free. Just look for a burgundy and cream tram and hop right on.

It comes nearly 24 hours after vandals targeted the busts of former Australian prime ministers in Ballarat, along with defacing a prominent statue of Captain Cook in Sydney's eastern suburbs.

The best times to visit Melbourne are between March and May and September and November. These shoulder seasons feature moderate temperatures and tourist crowds, plus lower airfare rates.