Miss Melbourne,

I've done the LAX - MEL trip a few times this year . . . and I think this is an easy solution for your desires (because I have done the exact same thing myself):

You can fly from LAX to SYD on UA (probably on flight 839) and hop off the plane, through customs & immigration and out of the airport in SYD. Tour SYD and then go wherever you wish on any domestic airline.

When you're ready to continue to MEL just return to SYD and continue on to MEL on the second leg of UA flight 839. It will be just like you never left the airport on your original arrival day.

When you do this you will get what's termed a domestic international boarding pass when you fly from SYD to MEL. It is a regular boarding pass with a giant orange "D" stuck to it - and you even get to go through the diplomatic customs & immigration queues.

Just let UA know you want to spend a day or ten in SYD before continuing to MEL.

UA has not once charged me for the stopover in SYD.

It is really simple . . . let me know if you need any more info on pulling off this scheme or places to go/things to do in SYD and/or MEL. I just spent one month in MEL (got back home yesterday) so I am up to date on things to do down there.

W