Hey, the North Island is good too you know...but yeah, the weather hasn't been so flash lately and if you can only pick one, then South Island it is. The weather changes everyday though, usually multiple times in a day.
As for what to do, it really depends on what you're looking for. If you're the sightseeing, tourist kinda person then there's no shortage of attractions - everywhere you look pretty much. If you're looking for thrill and adventure you could try snowboarding, skiing, bungy jumping, kayaking, jetboating, caving etc.
Don't count on bringing back any head-fi related souvenirs
Otherwise, things made from wool and sheepskin, chocolate etc. For places to eat, check out the Lonely Planet guide for NZ. They have little write-ups on most of the well-known places for good food regardless on how much you want to spend.
Aside from that, you could bring us some much needed headphone gear from the US!
Hope you enjoy your trip...