For happeneing city centers, I would give my vote to Sydney and Melbourne for sure, both cities are lively and have tons of stuff to see.
Some great things in Melbourne are
Center Point Tower
Watching the buskers from the lawn of the city library
Have a meal on the Tram resturant that takes you around the city while you eat
If you enjoy a gamble, the casino is a happening place
CAMBERWELL MARKET held every Sunday morning in the car park behind shops in Bourke Road you'll find all kinds of old and odd stuff there
Some great things to do in Sydney are:
Enjoying a pint on the patio of a pub at Circular Quay
Wondering around the Sydney Fish Market
Taking the ferries to check out the city scape ( very cheap)
The Sydney Harbour Bridge walk ( if you can get a reservation and want to pay the coin to do it)
The Royal Botanic Gardens are free and enjoyable for a relaxing walk
And you can not miss a noght around Kings Cross Sydneys " Red Light District"
Hope this helps ya some and never hesitake to ask a question here my friend there is always someone to answer!!!
Here is a list of hostel for the Sydney