NZ-North Island

Any hike in NZ will be wonderful - I wouldn't agonize too much about which ones are "the best" since that'll be a subjective call anyway.
If going down as far as Mt. Ruapehu consider staying a couple of nights at the Chateau Tongariro hotel - 4 star all the way (with a pool) and just outside the entrance to the National Park. There are too many beautiful hikes right outside the door to count, including a couple to nearby waterfalls.
In general, we've always found the I-Sites (tourist information offices) in any of the towns to be a wealth of helpful information. They'll have local maps and, more to the point, are staffed with knowledgeable staff who can point you to the prettiest hikes in the area based on your particular interests.

If you don't mind some obscure driving in the dark, the glow worms at this location are pretty neat and free

https://www.google.com/maps/place/Kakahi,+New+Zealand/@-38.9387775,175.3851853,5712m/data=!3m1!1e3!4m5!3m4!1s0x6d6b12499accd5f1:0x500ef6143a2d240!8m2!3d-38.9353042!4d175.3846055

We went to Te Puia which is the Maori cultural site and geothermal pools in Rotorua - it's a bit commercial, but we enjoyed it anyway. It's part of the Maori heritage and they're quite proud of it. If you can, try to take in a hangi in Rotorua - again, we wondered how commercial it would be, but found it quite enjoyable. A bit like the Polynesian Cultural Centre in Honolulu, but much smaller and focussed on the Maori story.
If you are hikers, I highly recommend doing the Tongariro crossing if you are able - you need a permit and to arrange transport to the start (busses waiting at the end to take you back). It takes all day and is a bit challenging, but the scenery is superb. Waitomo is quite fun - try to get on a boat tour. We drove to Napier after seeing Lake Taupo and stayed in a great art deco hotel there and signed up for a wine tour with Vines and Views that took us to 4 wineries ending with a picnic basket on a hilltop - all very enjoyable. New Zealand is awesome.