Life in Auckland: various questions

Hi!

I'm looking for a job abroad and I'm considering to apply to some opportunities in Auckland. Before doing so, I'd have a few questions about life in Auckland please.

Green area:

I'd want to know if there is a good balance between green area and buildings in Auckland, in particular in the centre and in trendy districts.
I used to live in Toulouse (France) where the trendy districts are 5/10mn walk from the river and grass ( Protected content ) and I can "suffocate" easily if there are not enough green area. I like big cities but I really need to breathe. For example, I spent 4 weeks in Dublin where there are a few big green area and then only buildings, it's not balanced and I didn't feel very comfortable.
Is Auckland this kind of town where you can walk 10 or 20mn without coming across any grass area? (and not just parcs because parcs often close too early)

Climate:

I'm not sure I understood how the climate is in Auckland, it seems to be both very sunny and rainy: how is it?

Hicking:

Is the North Island a good place for hiking? It seems the South Island is better, what do you think?

Thank you in advance for your help :)