New Zealand North Island destinations?

Hi,

We will be traveling to New Zealand later this year (during the New
Zealand summer) for a vacation. During that time I will spend several
days on the North Island. We'd be very grateful to hear your views on
the following potential destinations, and any others that you would
recommend, as we cannot, unfortunately, visit all of them. We prefer
adventure/outdoor activities over museums and wine-tasting, if that
helps at all. Also, if you can spare the time, we would love to hear
why you prefer (or don't prefer) these locations. You can recommend
them as (A) MUST VISIT; (B) visit only if you have time; or (C) skip
it!

Here are the potential destinations:

1. Wellington (flying into here first)
2. Auckland (flying home from here last)
3. Tongaririo Crossing - Tongariro National Park
4. Hamilton
5. Rotorua
6. Tauranga/Mount Maunganui
7. New Plymouth
8. Wanganui
9. The Northland/Cape Reinga
10. Other locations?

Thank you very, very much.

Dr. J