With all due respect to my Kiwi neighbours and your travel plans, I really think Auckland is a poor choice. The first thing you'll experience out of the airport is a teeming, seething mass of humanity in Auckland city that can sometimes resemble Shanghai, but with thousands of cultures colliding head on. It is busy, noisy, fumy, congested and a lot of footwork is required to get from one place to another. It gave me a headache one day, nausea the next (the latter being from food poisoning). Having said that, Aucky is central as a travel base around the north but problems with traffic flow (a lot of it in gridlock) will slow travel down. Find your own space.
Consider Christchurch on the South Island; hop over to the north on the Picton-Wellington ferry through the Marlborough Sounds.
Google is misleading: it is not so much the frequency of the HILLS that slow travel down, but their size. Factor in extra time to stop and gawk and definitely I recommend the road trip to Milford Sound the highest, starkest, boldest and wettest mountains that are utterly confronting in their size and profile. Everything else is just too touristy (including but not limited to Rotorua). Bay of Islands is oh-so-pretty but as in previous posts, it too, has been to the death as a tourist destination.