Under section 15 of the Immigration Act 2009 we will not grant you a visa, entry permission or a visa waiver if:
you have been convicted and sentenced to imprisonment for 5 years or more (this applies even if any of your offences have later been taken off the record),
in the past 10 years you were convicted and sentenced to imprisonment for 12 months or more,
you are subject to a period of prohibition on entry to New Zealand under section 179 or section 180 of the Immigration Act,
you have been removed or deported from any country, including New Zealand,
you are excluded from New Zealand under any enactment.
Sounds as though you'd be in the clear, even with the drunk driving charge.
There's also a good character requirement if you plan to stay more than two years.
http://www.immigration.govt.nz/migrant/stream/work/worktemporarily/