Hi,
I spend 4-6 weeks in Hawaii every year and I used to live in NZ.
What are you doing in Cali? 3 weeks is not long and there are plenty of good breaks there to keep you busy.
Hawaii is expensive and one week isn't enough to really do much but it is enough to see whether you do want to spend more time there in the future.
The A$ has just nosedived against the greenback, not sure about the Kiwi dollar but I remember travelling on NZ $ and it hurt big time, as Hawaii is at least 25% more expensive for everything than the mainland.
You would most likely stay in Waikiki and surrounds and surf the South Side. The North Shore isn't breaking in August.
Oahu is also the only island you can get to the surf without having a car, so that would be my main choice for first timers.
Taking your boards over from Cali will cost you heaps extra and really isn't worth it.
August is very crowded, peak season for tourists. I am not knocking it. Hawaii is amazing and my favourite place in the world and it's always great to spend time there.
There are cheap places to stay (backpackers/hostels) and so on and plenty of visiting surfers that you most likely can hitch a ride most days to the breaks (on Oahu at least).
If it were me, I would take a flight straight to Hawaii another time and stay on the North Shore in the winter months and hang out for a while and surf up there.
But then again, you could also do both

Either way, you cannot go wrong. Enjoy!