Turns out I don't know much about Auckland, but here goes...
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Caving in Waitomo http://www.waitomo.com/
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Aquarium, bit overpriced and old but there you go http://kellytarltons.co.nz/
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You can jump of this if it's your thing http://www.skycityauckland.co.nz/Attractions/Skytower.html
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Hot mud and party time in Roto-Vegas http://www.rotoruanz.com/
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Sailing and such http://www.explorenz.co.nz/SailNZ/index.html