I know this is a few months old now, but still might be useful to someone.
1. Auckland Model Citizens - A group based out of the Hobbymaster store in Ellerslie. Mainly play on Thursday evenings and Sundays.
2. Auckland City Guard - Mainly play at Spellbound Games in Highland Park on Wednesday evenings, but occasionally run games on Sunday afternoons in Newmarket.
3. Vagabond Games in the CBD run wargaming evenings on Tuesdays. Not a huge gaming space, but there are usually 2 or 3 games running.
Those are the ones I know off the top of my head, but I think there are a few other groups around different parts of the city.
The 'Warhammer 40k New Zealand' facebook group would be a good place to ask if you want to know more.