Quick answer
For a first New Zealand trip, resist the urge to see everything. Seven to ten days usually works best on one island. Two weeks can cover one island well or both islands quickly. Three weeks gives enough room for both islands without rushing every day.
If you have one week
For the North Island, base the trip around Auckland, Rotorua, Hobbiton, Waitomo and either Bay of Islands or Coromandel.
For the South Island, base the trip around Queenstown, Wanaka, Te Anau and Milford Sound, with one spare day for weather.
Avoid trying to cross both islands in seven days unless the trip is built around flights rather than driving.
If you have two weeks
A balanced first trip can start in Auckland, visit Rotorua and Wellington, cross by ferry, then continue to Nelson, the West Coast, Wanaka and Queenstown.
This is still a busy route. Cut one region if you prefer slower mornings, longer walks or extra time for weather delays.
If you have three weeks
Three weeks lets you include Northland or Coromandel, central North Island, Wellington, Marlborough or Nelson, the West Coast, Queenstown, Fiordland and Christchurch.
Keep at least two flexible days. New Zealand rewards the extra pause more than another rushed photo stop.