Probably not the best region to go to at the mo considering all the shit that has happened there this year. Christchurch is not in good shape, and wont be for a while. The skiing is average in my opinion (mt hutt would be the best), and there's pretty much little to no nightlife due to the city being under indefinite construction.
I would recommend you check out Dunedin (Otago). Really awesome city, solid university, decent nightlife, and the skiing is by far the best in NZ. Treble Cone, The Remarks, Coronet Peak, Snow Park, Cardrona...the list goes on. If you're focused primarily on skiing with studying on the side, this is the place to go. If you're more looking for the nightlife buzz and an outright epic city, with decent skiing relatively close, come to Wellington. Hands down the best nightlife and city in general in NZ (arguably).
What were you guys planning on studying?