Just came back from a trip in December, only running around the North island but all good fun.
Cant really add more than already mentioned above but from my trip..
Maybe Ferry up to Wellington and then get a hire car from there and go to Rotorua, the town itself felt a little ‘Blackpool’ to me but its a cycling mecca, worth at least 3 days or more exploring all the trails nearby.
Then I would recommend driving up to the bay of plenty and spending some time around there, followed by the the Corrinades then onto Auckland.
Found Auckland a little dull, maybe no need for more than a couple of days, try to get a ferry ride out the the surrounding islands.