Which city is best for active family to live in?

Auckland is best for these activities but as you said you do not want to live in expensive city then choose Huntly ( Around 80 Km south from Auckland ). Cheap as place to live all major cities within 30 minutes to 1.5 hours drive .

There are lot of Soccer clubs in South Auckland and that would be roughly 30-40 minutes drive from Huntly. you can also choose to live somewhere near Port Waikato or Pukekawa but they are real far from main motor way. On the other hand beautiful and safe places than Huntley

Auckland is nice in many respects and would suit most of your requirements but property-wise it has become extremely expensive. Being a big city (certainly in NZ terms) it is also suffering badly with traffic congestion. Distance wise the airport drive should be easily within an hour from anywhere in Auckland but only at specific low traffic times.
There are many beautiful cities in NZ and New Zealanders are an exceptionally active bunch so I'm pretty sure they would all meet your sporting needs.
I stay I Wellington (dubbed the best little capital in the world) and it truly is a great little city! Beautiful and has everything you could want. Has busy rush hours but nowhere near as congested as Auckland and propert prices have remained far more reasonable.
You may want to check flight arrangements though as the airport does not cater for many long distance flights.

I used to live in Toronto so understand the climate there. Dunedin is a university city with a great cultural/sporting scene. It has cool winters, but nowhere near as cold as a Canadian winter. It is also the cheapest of the main cities to live in and doesn't have the provincial feel and look that most other cities outside Auckland and Wellington have. With 20.000 students making up the total population of 110.000, it has a very liberal approach to things. With its amazing Victorian and Edwardian architecture,it has the feel of a European provincial city (not a colonial one)
Check out their website. It's also in easy reach of the most spectacular scenery in the world as well as Australasia's top alpine resort, Queenstown. The South island has a different feel to the North Island. The living costs are a fraction of those in Auckland with its congestion and expensive rents and transport costs.(not a place for a family)

dunedinnz.com/visit/home

Ceidrik Heward