Welcome to New Zealand! I myself am from the North Island (Taranaki Area) but now live in Christchurch and have done since the earthquakes. I think you have come to town during what seams to be our annual storm right after Christmas. Wait half a month and Christchurch will start going into a no rain no cloud in sight dry period. If you get a chance make sure you head down to Milford sounds. I did a blog a long time ago of our travel there but here is 2 photos that stood out:

The weather changes rapidly here due to the contour of the skinny islands. Have Fun in NZ and let me know if you need any suggestions!