If you want to ski in the South Island around Queenstown/Wanaka there are 4 fields that are accessible : The Remarkables, Coronet Peak, Cardrona and Treble Cone. I've skiied all except Treble Cone and have found them all pretty good, although I tend to prefer Coronet Peak. The Remarkables is the closest to Queenstown (30-45 mins drive) and has more beginner slopes (the pistes are split about even for Beginner, Intermediate and Advanced). Treble Cone is the closest if you're staying in Wanaka.
There are plenty of hotels to stay but I haven't been living in NZ for more than 8 years, and as such haven't skiied there since. So I imagine the prices have gone up since. Queenstown is quite pricey regarding accommodation but I was there on holiday in January and could get a reasonable double room for around NZ$100 per night. Although I guess the prices would be more in winter and would book up quicker. Of course as Queenstown is the adventure capital of NZ there are plenty of activites to keep you amused in the days you decide not to ski.
There are loads of other fields further north in the South Island, Mt. Hutt isn't too far from Christchurch and if you stay in Mt. Cook or Hanmer Springs (both picturesque places), there are several fields you could try. I have only skiied the 3 I mentioned from Queenstown so I can't comment on their quality.
As Bonbon has mentioned, the North Island fields are located on Mt. Ruapehu, they are Whakapapa and Turoa. They tend to get quite crowded during the school holidays but are both quite large fields (400 hectares) by NZ standards. You can stay in Ohakune if you want to go to Turoa whereas Whakapapa Village has places to stay on the mountain. Further afield (but still not a long drive) are Turangi and Taupo which are much cheaper.
Another website that has a lot of information is:
http://www.snow.co.nz
One other thing possibly worth mentioning is that in Europe and North America you tend to have to worry about trees on the piste. In NZ it's rocks. Oh yes, and Mt. Ruapehu is an active volcano - but don't worry, it hasn't erupted for over 10 years!