If you are planning to go skiing in NZ, of course South Island would be a lot better than North Island.However, with a bit of luck, we went to Whakapapa last Septmeber and it was ok. Just don't compare it with Sappora, Japan.
What course do you want your daughter to do over a few weeks?
A lot of the English language schools (actually most of them) won't accept your daughter as she is only 8 years old. They prefer the students to be at least 15.
Maybe you could help her to enrol some 'School Holdiay Programmes', they are designed for kids 5-13 yrs old, noramally 1-2 weeks. They are not a proper sit down classes, but a bunch of kids with the same age and having lots of activities together with lots of funs, so apart from learning english, your daughter could also mix and mingo with kiwi kids.
So many companies running School Holdiay Programmes, as not sure which area you and your family will be going this July, I could only forward the YMCA one to give you some ideas: