Hello hello!!
I'm a Canadian that's been living in Queenstown, NZ for the past 4 years. Queenstown is a small resort town in the South Island, about 6 hours from Christchurch.
From what you've described, I'd say you'd be pretty set with either Wellington or Auckland.... or, just as another option, Dunedin? For snowboarding, the South Island is your best bet (Queenstown/Wanaka area) but you can also get to Mt Ruapehu from either Welli or Auckland in about 4 hours. Both cities have really good live music scenes (most places in NZ do!!). I'd say if you like "big" cities and a bit warmer weather head for Auckland. If you like a bit more of the cafe/arty/music culture (and wind!) head for Welli. You can get to surf from either city.. obviously warmer up Auckland way. I'd say I prefer Wellington but it's totally a personal preference thing and I'm not that keen on big cities.
I'm not totally sure but I think cost of living for a student would be similar in both cities.
Hope that helps a bit and let me know if you have any other questions. I totally recommend coming to NZ... amazing place with loads to see and do and amazing people.
All the best!
