Days1-2-land in Sydney at 6am, explore for 2 days, fly to Cairns at 7.30pm next day.

Days3-5-Palm Cove-Daintree Air Lizard Island tour, Peter Baxendell Daintree/Cape Tribulation tour, Ocean Spirit Michaelmas Cay tour.

Day6-Fly to Christchurch.

Day8-explore Christchurch.

Day8-Tranzalpine to Greymouth, rent a car, drive to Fox Glacier.

Day9-helihike, walk arond Lake Matheson.

Day10-drive to Queenstown.

Day11-coach/cruise/fly Milford Sound.

Day12-Glenorchy Air Mt. Cook flight.

Day13-Dart River Safari.

Day14-explore Queenstown.

Day15-fly back to LA.

Sydney is a big place with tons to do and see. We loved it and wished we stayed longer than a one week.

You can see Christchurch in a few hours.

Tranzalpine takes all day, nothing much in Graymouth. Instead,
rent a car in Chrischurch and drive West
nela

sorry, the train ride on Transalpaine is about 4 hours ( it seemed longer) but you have to get to the station in Christchurch well ahead of time to get a ticket. Also, the train station is not in town.

I think that if you cannot give more time to North Queensland and Sydney then I would skip it altogether. You will miss a whole day with jetlag and one day in Sydney is not enough. Neither have you any time if the weather is not good for either flying or a reef tour. As one other poster said Christchurch can be seen in a few hours. Similarly you can see all of Queenstown in an hour.

We are just back from NZ.We followed a similar route- some comments : depending on your interests I would suggest picking up the car in Christchurch driving via Hamner Springs to Pancake Rocks and down the coast to Fox Glacier.We did the train trip. You need to be at the station before 8am it is on the outskirts of town. We did enjoy the train but wouldn't say it is essential. You definately need a full day in Fox to allow for weather changes and the chance to helihike or recommend 1/2 day hike with Foxguides- it was excellent! We were also fortunate to get great weather to fly on helicopter.
In Queenstown we basically needed 1/2 day only to do Gondola ride and luge. Also drove out to Arrowtown and watched Bungy Jump before our flight as they are both close to airport. The Dart River Safari - a must do !! We loved it. What exactly are you planning for in Milford as it is a long!!! way from Queenstown? You may need to stay at Te Anau. Also consider Doubtful Sound . We did the overnight boat trip which for me was the highlight!! I would also consider other comments made re- time and jet lag.