I did a day trip to Waiheke Island and saw the Aukland Museum, as you suggest. In addition, I did a couple day tours out of Aukland that were good. My trip was fall of 2019 before Covid disrupted the world, but I still see them posted on TripAdvisor.
One tour was to the Hobbiton movie set. I'm not really interested in The Hobbit and hadn't seen the movies, but the tour was still enjoyable. It's quite popular. There is another tour that combines that stop with the Waitomo glow worm caves in Rotorua. I visited Waitomo on my own - recommend it as an interesting stop. ( At least for me, the glow worm caves were interesting.) Another day tour I see listed includes Waitomo and a Maori area of Rotorua that I visited on my own - again, both good stops. (I stayed in Rotorua for around 4 days and Auckland about 5 days.) I also took a day tour to Coromandel from Auckland.
I booked directly with the companies offering the tours, not thru TripAdvisor. As a solo traveler, a booking for one person was not a problem direct via the company's website, but with TA, it seems they want at least 2 travelers.
Another day, I took a ferry to Tiritiri Matangi and had a guided birding hike. I'm not a bird watcher, but I did enjoy the day - light hiking and lots of bird species we don't see in the US. I took another ferry another day to Rangitoto Island. You can easily hike up the dormant volcano and hike around the island before catching the ferry return.
I'm not sure if any of those are "must sees". If you aren't going to Rotorua during your time in New Zealand, I think that might be a day trip to organize. Different options from Auckland.