We have done trips to the South Island last year and the North Island this year.I have posted trip reports for both trips.
Our 3 week South Island roadtrip
Flew to Christchurch then
Geraldine.
Lake Tekapo
Twizel, Lake Pukaki, Mt Cook.
Omarama.
Lindis Pass, Cromwell.
Kawarau Gorge, Queenstown.
Te Anau.
Doubtful Sound.
Milford Sound.
Kingston, Lake Wakitipu.
Arrowtown.
Crown Range, Wanaka.
Haast Pass Road, Haast.
Fox Glacier.
Franz Josef Glacier.
Hokitika.
Arthurs Pass.
Flew out from Christchurch.
Our total cost inc vehicle hire and fuel, overnight stays, coach and cruise tours in Fiordland, all food and drink and all other miscellaneous was about USD3600.
Our 3 week North Island roadtrip
Flew into Auckland.
Waiomu (Coramandel Peninsula).
Te Aroha.
Hobbiton.
Rotorua.
Taupo.
Whakapapa Tongariro National Park.
Whanganui, Kai Iwi.
Patea Beach, Waitara, Mt Taranaki/Maketawa Hut.
Tongaporutu 3 Sisters and Elephant Rock.
Mokau.
Otorohanga.
Huntly.
Piha Beach, Muriwai Beach.
Matakohe.
Whangarei.
Paihia, Kerikeri, Hole in the Rock cruise Bay of Islands,
Waipu.
Flew home from Auckland.
A little less costly than the South Island total of USD3200 All up.
Certainly not comprehensive tours of either Island but we saw heaps of great places, did loads of interesting things, enjoyed ourselves madly.
Check out a road atlas or google maps to see where we went. It's a long list but if you do internet searches on the above locations you should find plenty of things of interest.
The majority of the places we visited tick the natural wonders box.
Rotorua certainly has plenty of Maori cultural experiences but there is also plenty in Northland around the Bay of Islands. But really you will pretty much be tripping over culture, history and natural wonders wherever you go.