If you're wanting to get a local South Korea SIM card (which would be your cheapest option) you'd need to find a network there and make sure the device is compatible.
Alternatively, you could get a Vodafone NZ SIM card, and use it for roaming. This would cost $10 per MB for prepay or the Zone 2 Roaming Rates on Postpay which can be found here: http://www.vodafone.co.nz/daily-roaming/
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