NZ travel plan & how best to do Mount Cook

Hi! I’m planning a trip to New Zealand in mid-May for about 2 weeks, and would like some feedback on my itinerary, as well as advice on the best way to visit Mt Cook.

I’m a solo female traveler and not renting a car.

Current Itinerary:

• Land in Auckland from the US, will stay for 2 nights (including Waiheke day trip)
• Fly to Queenstown
• Stay in Queenstown for probably 2 nights, I’m interested in visiting nearby places like Arrowtown and Glenorchy
• Travel north to Mt Cook / Tekapo
• Join a South Island group tour starting in Tekapo, going to:
  • Queenstown again
  • Milford Sound
  • Wanaka
  • Franz Josef Glacier
  • Christchurch
• 2 nights in Christchurch, possible day trip to Akorua or Waipara Valley
• Fly back up to Auckland for 1 night before flying home

Is there anything I am overlooking? Is there anything weather related I should be aware of?

I also would like some help regarding Mount Cook.

It looks incredible and I’m really excited to go, but I’m struggling with logistics without a car. I’ve come up with 3 options:

Option 1: Stay overnight in Mt Cook Village

• Bus from Queenstown to Mt Cook ($200NZD, only 1 per day)
• Stay 1 or 2 nights (hotels here will be the most expensive option)
• Have time to do the glacier boat tour
• Bus from Mt Cook to Tekapo to meet my tour ($200NZD, only 1 per day)
• Thoughts:
  • This seems like the ideal experience, but I am not sure how easy it will be to get around the park without a car
  • More importantly, I want to make sure I will be able to enjoy the nature safely. I am comfortable with solo nature walks, but I am not comfortable scaling a mountain by myself. Will I feel limited there?
  • This is the most expensive option, but I am ok with that if it is the best experience

Option 2: Base in Tekapo + day trip to Mt Cook

• Bus Queenstown to Tekapo (~$76-96NZD)
• Shuttle tour from Tekapo to Mt Cook ($150NZD) the next day
• Thoughts:
  • Only 5 or so hours in the park, not sure that is enough
  • Less immersive than staying overnight
  • This would give more time in the park than the intercity bus, which is only once a day each way and costs more

Option 3: Guided transfer/tour from Queenstown to Tekapo, stopping in Mt Cook

• Full-day guided tour for $380 NZD
• Includes many stops that look great on the way, then Mt Cook for about 3 hours, ends in Tekapo
• Thoughts:
  • The easiest option logistically, but least time at Mt Cook
  • Could in theory go back to Mt Cook the next day with the shuttle, but that is a ton of unnecessary travel

With all that said, I essentially am trying to figure out-

1. Is staying overnight in Mt Cook Village worth the extra cost/logistics instead of just doing a day trip?
2. Would ~3–5 hours in Mt Cook feel too rushed?
3. For a solo traveler in May, is Mt Cook Village easy enough to navigate without a car, or does it feel limiting? And will enjoying the nature feel safe solo?

Thank you in advance! I appreciate all advice, especially from people who’ve done this without driving!