Try not to go via AUS as there is usually an over night and you'll have to drag all your luggage back and forth unless you can find a locker at the airport..
Ditto. I've heard stories about flights in/out of AUS having severe baggage limits, so that's another reason to avoid bouncing through there.
If you need to kill time, do it in Sing.
Changhi Airport in SIN is fabulous. Lots of stuff to do and a transit hotel inside the security area if you have a long layover. Caution! When I was there in January we left the airport to have lunch with a local friend. When we returned we discovered the Air Niugini check-in counter didn't open for another couple of hours (it only opens a few hours prior to the flight) so we had to kill time before we could get our boarding passes and be allowed back into the security area.
Another (not so well known) option is Manila. The direct flight to Port Moresby is 5 hours.
The January trip was made on China Air (who are great) and Air Niugini. On the way there we flew SFO-Taipei-Singapore-POM, and on the way home it was POM-Manila-Taipei-SFO. The way home was more direct and faster and that way we didn't have to overnight in Port Moresby. But the Manila airport is crowded and pretty much a sh*thole; it's considered one of the worst airports in the world, so be careful.
-Gina