Welcome to NZ---
Yes, you're finally here after all the steps and anticipation!
Recover your sleep, slow down to take it all in and just start exploring once you have your home base established.
Yes, lots of hills and walking for me too I found when I first arrived which was good (lost 4lbs in the first month or so due to more walking!) plus its an opportunity to see things on foot vs. a car.
Great to have someone to share it all with as well as I imagine it would be quite difference vs. doing it alone as I did.
Its a beautiful night in Auckland tonight and starting to get a nice pinky sky