New Zealand in 10 days, for 2 weeks

It's been a few years since I visited NZ ( cycled 1700 miles over 6 weeks, covering both islands in 1983).
My advise would be to see less of the cities and more of the country.
Places that stay with me after all these years are;
Rotorua for the geothermal features and Maori culture;
Lake Taupo - geothermal pool and the night along the river camping with a NZ family;
The Beehive of Wellington - their government building I believe;
Ferry to Picton across the Cook Strait;
the Punakaiki (pancake) rock formation along the coast between Westport and Greymouth;
the church in Christchurch (since damaged in one of the recent quakes);
the road to Mt Cook, and hiking atop a glacier (probably since melted);
Milford sound and Mitre peak;
the unexpected overnight stay at a sheep ranch on the south island, when all we were looking for was water.
Enjoy.

I cannot tell from your narrative how much time you have where. But if you can spare 2 nights at Picton, I highly recommend this eco-lodge, accessible by water taxi from Picton:

http://www.lochmara.co.nz

And I would ask, why three days at Christchurch? What do you intend to do there? Take two days uand go to the place I suggested. Or take the train down the coast and stop at Kaikoura to swim with dolphins.

https://www.dolphinencounter.co.nz

Agree with commenter Michael E about spending less time in the cities. In February 2018 we spent 25 days mostly traveling in a Sprinter van (over 3000 miles logged), once on a train, a helicopter to Franz Joseph glacier, numerous boat adventures and one jet to get around the two islands and there still wasn't enough time to do both islands justice. Suggest taking one island at a time, making two visits.

If you're going to do both, suggest you check out the Coromandel Peninsula, (about 3 hrs. drive south and east from Auckland) instead of spending 3 days in Auckland. Lots of lush forest hiking trails there and nearby scenic shorelines (Cathedral Cove) at Hahei beach.

Consider going to the historical museum in Wellington (free!) while you're there instead of the one in Auckland ($30). Take the funicular up the hill and trails back into Wellington to the harbor trail.

You might wish to re-think your time allotment for Christchurch. They have a nice botanical garden and museum, but not sure what you would do for three days.

If you can, go to Milford Sound and take the overnight boat cruise (leaves in the afternoon, returns the next morning). A great visual nature film shot by the expert local helicopter pilots in Fjordland, invest in a DVD copy of Ata Whenua Shadowland (Amazon). Absolutely awesome. You won't regret it. It might make you change your original plans!

Check out Black Sheep Touring Co. for other itinerary ideas. www.blacksheeptouring.co.nz

Best of Luck!
Enjoy

I hope you look at YouTube videos of Queenstown before you rule it out. It is an amazing place.

Thank you for your responses.
Maybe I did not give enough information about our trip.
We are not going to just sit in Auckland or Christchurch for the allotted 3 days. We want to have a place to stay where it isn't pack and unpack each night. We plan on going to Mt Taylor, Lake Heron/ Coleridge. but keeping our "base camp" at one hotel.

As for Auckland area, we will be on the West side of the island, but close enough not to have to drive far to get to the airport when we depart.

We are contemplating Kayaking vs Whale/dolphin tours. But I was unsure where would be the best locations for that.
Glow worm caves and Hobbiton are on the list as well as some beaches. But I was looking for more insight.

thank you for any more input guys!