Christchurch is located on the east coast of the South Island of New Zealand and is a common gateway city for many of the Southern Island ski resorts as it is the closest international airport for most.
If skiing futher south near Queenstown or Wanaka then you can get a connecting flight from here or there are regular buses as well.
Late afternoon flights from Australia arrive about 11.45 or midnight. By then the buses have stopped running and a taxi into town is pretty expensive. Sleeping in the airport is possible, it's quiet, the security guards will not hassle you and there are good free showers!
If you arrange it beforehand, some transport operators will pick you up from the airport at about 7am and take you skiing. Operators that go to the Club Fields include: Black Diamond Safaris Snowork Tours
You might end up in Christchurch for a day or two at the end of your holiday, for whatever reason. YMCA have two good hostels in the centre of town, Rolleston House is probably the best. If the weather is good, consider hiring a bike, the city is flat and there are some nice rides along the Avon and Heathcote rivers. Or go for a couple of hours ride up onto the Summit Road of the Port Hills, great views. Mountain biking in the Bottle Lake Forest. The city has lovely botanic gardens in the centre of town, especially in spring. If the weather is bad, consider going to the museum, or The Roxx indoor climbing wall. A fun day would be to take a day bus pass, and use the city's network of buses. A trip on the number 10 bus to the Sign of the Takahe and Victoria Park for a gentle stroll up the hill is a good day out. Followed by another ride back to town and out to Sumner beach, where there are seafood restaurants and pizza eateries. Lyttelton is the port of Christchurch, a quaint little slightly-bohemian community. All sorts of eating options in great restaurants.