You may under-rate the challenge of the Routebourne track. Recently there was a tourist hiker found alive after being lost for 3 weeks; it is much more serious wilderness than Sierra Nevada & Yellowstone, though Wyoming and Alaska could be comparable in parts. If you do decide to hike there, rent or buy an EPIRB esp with a 5 year old. It is hard to evaluate until you see it for yourself, really beautiful country but also very challenging much of the year.
As for attractions, the volcanic activity around Rotorua is stunning even today (was the 8th wonder of the world a century ago until an earthquake destroyed the terraces). Very easy hiking but with a lot to see.