Far and away the best skiing when there is good snow cover is Whakapapa on Ruapehu in the north island. Ohakune, the town that supports Turoa on the other side of Ruapehu is worth staying at for partying, it is a bit barren socially at Whakapapa.
Best of the rest, Wanaka - Cardrona for cruising and Treble Cone for some good steeps, if there is enought snow. Wanaka for good fun and a busy social scene.
Don't waste your time in Queenstown, good fun, but over-run with hardcore tourists, and unreliable snow at Coronet and Remarks are sketchy as well.
Mt Hutt near Methven will give you good snow from June through early October, and Methven is a fun town to live in. Mt Hutt is a bit on the boring side though. Good as part of a tour.
But...one of the great secrets of NZ skiing, the club fields in the south island. There are some gems in the southern alps, with the greatest atmospheres, people and good skiing (epic hiking) to be had. Try Broken River, Mt Olympus, Craigieburn, Temple Basin, Porter Heights, and Dobson.
An awesome itinerary for 3-4 weeks of skiing:
Week 1: Whakapapa and Turoa, head down to Christchurch, rent a camper van, and spend Week 2: Mt Hutt, Porter Heights, Craigieburn, Broken River, Mt Cheesman, then head south to Wanaka for
Week 3: Treble Cone, Cardrona, Dobson
Week 4: See Q'town and ski Remarkables (go jetboating as well).
The season in general in NZ is south island mid/late June - early October; North island early July - early november.
Have a great time, there isn't another country on earth that comes close to NZ.