I was born and lived in NZ for 24yrs. Here’s an agenda. Fly to Auckland, drive north to Russell (Bay of Islands). Drive south thru Auckland to Coromandel Peninsula (stay Whangamata). Head south to Rotorua, then Taupo and keep on all the way to Wellington (you have seen the best of the NI. Take car ferry to Picton. Then south to Kaikoura. On to Christchurch. Drive west over Southern Alps to West Coast, turn left (!) and see Fox and Franz Joseph Glaciers.