Ideas for 14 days New Zealand trip for students from Europe

Hello! So we have quite a weird situation here and we are seeking for advice on how to best use our time in New Zealand to get the most out of it.

In February 2024 two of us are travelling to New Zealand for a month, third person is coming later and will stay with us for the last 14 days. First 14 days will be spent in Auckland. For the first 14 days there won't be as much time for sightseeing because work etc. so we are looking for reccomendations on what to do around Auckland (we don't want to do anything too big because we want to do major sightseeing tours when the third person arrives).

Is it worth to visit both islands in 14 days and if it is, would it be best to rent a campervan or to sleep in different air bnb's as we move around the country? We are leaning towards renting a campervan because it saves a lot of time because you can just camp instead of going back and forth to your apartment.

Perhaps it would be best to fly from Auckland to Queenstown and spend majority of the time on the south island and then spend the last few days visiting places on the north island?

We are all very active people so we don't really care about visiting wineries etc. instead we are looking to do a lot of hiking and other (adrenaline) activities. We saw that prices for water taxies for major sightseeing tours are quite expensive so if you know anything cheaper or hidden/less known nice places that are close to major sightseeing places please let us know.

Where could we see seals, kiwi birds,... ? Many companies offer tours for seal watching but it is quite expensive for our standards. Is it possible to see them on a beach for free?

If you have any tips or reccomendations for itinerary or anything related to travelling New Zealand please let us know.

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I apologize for my grammar as I am not a native speaker.

Looking forward to your responses! :)