Actually Happy Valley at Whakapapa is probably the most extensive beginners area in New Zealand. Though it's true that snow quality can be marginal, especially early in the season.Other than that I reckon the learners area at Remarks is pretty good and under-utilized for the most part.
Hard to beat Cardrona ESP if you need to place kids in child care. Cardi has extensive beginner & inter slopes, wide runs & good chairs. Oh and pretty reliable cover c/w other southern fields. Agree select areas on Coronet & Remarks are good too but I reckon Cardi is a tad better overall. better still go to a few of them
Have to second vote for Cardrona. VG conditions for Beginners/ Inters with some tasty stuff for others as well, depending on conditions. Also consider Roundhill and Mt. Dobson if going South from Christchurch to QT. Go to NZ South Island. Best to stay in Wanaka for easy access to Cardrona. Flying out of QT is the way to go.
There's a season pass for $A295 (adults, $A175 kids up to 18 iirc) at the Nth Island's Ruepeho/Whakapapa/Turoa (mid way between Wellington and Auckland) which can add (for a tad more?) Cardrona on as well.
Check out those mountain's webpages. Or google Endless Winter Resorts of the World Pass, with umpteen main and small ski fields to ski in NZ .... and then you can even ski Winter Park Colorado free or half price in Banff Lake Louise Canada.
Happy Valley is indeed good (though can be crowded) but after that there is a bit of a jump in difficultly, as the top of the rock garden has a few killer turns that you need to navigate, and the next easiest place requires T-Bar skills (The Waterfall).
If you can learn there though, you can ski/ride anywhere.