If you would like to see the big cats in action ie. not sleeping then it would be a good idea to go see these (tigers, lions, cheetahs) either early in the morning just after the zoo opens or later when the zoo is about to close. The Tiger cubs in particular come out in the afternoon and have a play and usually get fed and the Cheetahs are always up and about early in the morning when they get fed (i think).
The same goes for the rainforest (siamang gibbons, spider monkeys, golden lion tamarins, bonnet macaques etc) as it gets very very busy during the middle of that day and it becomes very hard to get close enough to see anything unless you are very tall, especially with the tamarins.
Most of the zoo gets very busy at midday which is to be expected so if you were to go to the zoo at opening (9.30am) and check out the cats and the most popular enclosures (burma the elephant, rainforest, hippo river etc) as early as possible and save the smaller, less popular, more hidden enclosures (doris the alligator, reptiles, birds) for later when there are more people in the zoo it should work.
Also check out the list of encounters and get to the ones you are relly interested as early as you can especially if it is a popular encounter (though most encounters are popular, some more than others) such as the elephant, lion and Tiger encounters. Some encounters have only small spaces for people to fit in to (such as the tiger, lemur and in particular the native fauna encounter) so you would benefit from arriving at these even earlier (1/2 hour before maybe)
If you have never fed a giraffe before then the Giraffe encounter is something not to miss, its a cool experience.
At the moment Auckland Zoo has a very cute little baby boy Hamdrayas Baboon that if you catch on the right day, and time of day is a real little character and fun to watch playing around.
If you go to the zoo on a tuesday then make sure you go to the NZCCM
vet team encounter; it gives visitors a unique opportunity to watch the zoos vet team in action.
The zoo is rather proud of their breeding family of Orangutans and 4 year old Madju is a real cutey so have a look at them too.
Oh and make sure you have a look at our NZ sealions, Fur seals and Californian Sealions for the underwater viewing window, its pretty cool.
Well thats all I can really think of at the moment.
Hope it helps
JTC