NZ trip plan

Hello all - I’m travelling to New Zealand from the US for the first time. I’ll be there from Sunday May 24 - Sun May 31. I want to make the most of my time but also take it easy - I’m a relaxed traveller who doesn’t want to spend every minute doing some activity. I am Muslim so I have dietary restrictions (halal only). May 27 happens to be the biggest Muslim holiday which I’m planning to spend in Auckland. Would love your feedback on my itinerary below. Am

I doing too much? Am I missing out on something?

Day 1 - May 24 - Arrive in Auckland and explore the city

Day 2 - May 25 - Ferry to Waiheke Island. Spend the day here and back to Auckland in the evening

Day 3 - May 26 - Rent car to go to Rotura. Checkout Champagne pool, Geysers, Redwoods forest walk. It says it’s a 3 hour drive each way so I’ll be driving 6 hours. Not sure if it’s worth it or I should take a flight.

Day 4 - May 27 - Celebrate Eid in Auckland, leave for Queenstown

Day 5 - May 28 - Milford sound. I’m thinking I’ll take the guided tour, avoids driving for a long time. Is this a good idea? I also plan to do the Milford sound cruise. Back to Queenstown

Day 6 - May 29 - Queenstown + Arrow town. Skyline Gondola, lake wakatipu, onsen hot pools. Will rent a car here. Stay in Queenstown.

Day 7 - May 30 - Drive to Mount Cook. Stay in Twizel… is this worth it? I’m not sure I’d wanna spend hours hiking here.

Day 8 - May 31 - leave early morning and drive to Tekapo then to Christchurch. Drop off car at the airport. Leave Christchurch. Is it worth spending a night in Christchurch?