Skiing in Australia is far from good. It's expensive, over crowded and poor value for money.
New Zealand pretty much rules the Southern Hemisphere for skiing and I have skied all bar a couple of private fields in the past.
My take...
South Island.
This is the Mecca of alpine skiing - you have the resort type fields - Mt Hutt close to Christchurch, Mt Dobson about half way between Christchurch and Wanaka, Cardrona and Treble Cone near Wanaka and Coronet Peak near Queenstown.
Wanaka is about a 1 hour transfer from Queenstown and is beautiful, but is not the tourist area such as Queenstown. There is a resort we used to swap timeshare weeks for (it is also a hotel) -
Edgewater which is brilliant. You can get chalets with 2 rooms - this would sort out the kids and a 1 room for mum & dad?
My opinions on the ski fields:
Starting south heading north:
Coronet Peak - usually quite crowded (not by Australian standards though) and is alround pretty awesome. There is also night skiing [as if your leg muscles will take it after a hard day!]
The Remarkables - again, crowded due to proximity to Queenstown, - pretty good beginners field IMHO
Cardrona - closer to Wanaka. This is IMHO the best ski field I have skied on in NZ. It has some pretty hairy black runs - the captains basin is brilliant blue area - no as suited for beginners as the previous 2 but still a pretty awesome place. Some amazing off piste available if you don't mind a pretty decent climb
Treble Cone - close to Wanaka. A great laid out field - we used to call one run the High Way - a wide "road" from the top of the high speed chair to the bottom zig zag down - great for beginners to get the fear of speed out of themselves - a close second for the title of best in the South Island. There are also some amazing Black runs with some pretty breathtaking narrow chutes to drop in on one of the T Bars
Ohau - when I last skied there, it was one chair and a rope tow (or T Bar) and a pretty awesome field. It is steep and scary - brilliant! No good for beginners. The Camp and Hotel at the base of the field is good accommodation - put your nerves in a jar before driving the road up - We chose the transfer bus so we could keep out eyes closed the whole way! :redface:
Potts - access to the runs by snowcat! Beginner free zone
Mt Lyford - the only time there it was closed, so maybe someone else can update this
Mt Hutt - Proximity to Christchurch, crowded (by NZ standards), an excellent cross section of terrain - well worth skiing there
Rainbow - this is a Nelson area field - the drive to the field through the Forrest with Fords and a raging river next to the road, through farm land dodging cattle then finally to the ski field can be more exciting than the skiing - the views however on a clear day will have you believing that this is truly the most beautiful place on earth - honestly. (note: Toyota corolla, river ford, don't stop for photo opportunity!)
there is also a myriad of club and small private fields in the south island - many are uni clubs, some have public admission - google club skiing NZ and you should find a few interesting bits and pieces.
North Island.
Taranaki - club field - huge trek from carpark to pomel
Mt. Ruapehu
This used to be my local field. National Park is a small town close to the northern field Whakapapa and I recommend the National Park Hotel for cheap accommodation.
Turoa - an awesome ski field - some brilliant powder can be had after a cold southerly, great terrain, and a full suite of beginner through to advance intermediate runs. Huge field, great facilities
Whakapapa - "the magic mountain" - and it is! If I was in the OPs position, this is where I would look to Ski. The runs are awesome from green to 2xBlack - the national downhill (put me in hospital!) is so much fun, and I believe the largest ski area in the Southern Hemisphere. Happy Valley dedicated beginners area (meaning no coughs come screaming through) with I believe a brilliant ski school available. Accommodation available to clubs on the mountain. The carpark is around the same height as the highest run in AU, so there is always lots of snow!
I would suggest looking for accommodation in National Park (15 mins) or Turangi (50 mins) or if the AMEX is good for it, Skotel is pretty good as well (maybe not family friendly). There's also a caravan park with cabins at the foot of Whakapapa.
I hope this helps