Most of people tend to think of Auckland as the the capital city of New Zealand, when in fact it is Wellington and it has the added virtue of being the most southerncapital city in the world. Skiing is possible in mountain ranges that surround Wellington.
The city continues to recover from the fairly recent earthquakes, so Christchurch definitely warrants a visit, as plenty to do and see.
Watch out for the sheep wandering onto the road!
If off to Oz later in your trip, then check prices here:- Australia.