If you are a Star Alliance FF then a good route is LAX-AKL-MEL or SYD on NZ. The MEL route will net you about 300 more miles then the SYD route for the same fare. I use a consolidator in NYC that can book D class for around $4900. Booking this way will net you an additional 25% COS bonus.

I go down under 4-5 times a year and all of the cities you are suggesting are very nice and very different. For a short stay try 3 days in Sydney (acutually reminds me of Chicago except better weather, safer and much less expensive) In SYD Check out the Sydney Aquarium (any closer to a shark and you'll need a flashlight), the ferry ride to Manley (bargain of the century) and of course a walk through the Botanical Gardens. For dining try the Pier in RoseBay. Not cheap but memorable. (count on $100+ AUD + booze and tip PP)

A cheap 1 hour flight to MEL will cost you around $150 AUD return on Virgin Blue. Quantas has competitive fares but they are not available on every flight.

In MEL A walk along the St Kilda's Promenade at sunset is a must. (Sunset is as good as Key West without the crowds), The food court in the South Bank River Center Mall is a model of efficiency and variety. (Cheap eats and very good) Upstairs the retaurants are pricier and not as good IMHO)

In both cities the Starwood properties are wonderful. The Westin Melbourne is my favorite Business Class hotel in the world. Not as opulent as the St. Regis in Rome, but bright, clean and classy. In Sydney the bargain of the century is the Four Points Sheraton on Darling Harbour. It used to be a Nikko that Sheraton took over and maintained in its original condition. If you get any harbour view room, you will be treated with a world class view, and you'll be walking distance from all sorts of neat little cafes and shops.

Enjoy