Mark,
The must see courses in Australia are RM, KH, NSW, and Barnbougle Dunes. If you aren't going to take a day out for BD, then I would try to get down to Mornington Peninsula for St Andrews Beach and/or National Moonah. I have only been down once so I would pay most attention to the advice of the Australian gents.
In New Zealand, the 3 courses to see are Paraparaumu Beach, Cape Kidnappers, and Titirangi. Seeing all 3 of these will not be possible if you don't feel like doing a bit of driving.
Regardless of where you are going to play I would make it a point of getting together with the local GCA'ers. Those guys were most responsible for me having the greatest golf trip of my life.
I still need to finish my review of the courses, which I have been pathetically slow at getting around too. If you look back there are some great reports from Philip Gawith, Matt Cohn (see his opinion piece), and I had a few threads about a year and a half back asking the same stuff you are and had many great responses.
Happy planning.