My husband has a business trip to Auckland in April and we will be arriving a day early and would like some ideas for interesting sites in the city. Thank you.

We enjoyed our visit to the top of the Sky Tower.

What are your interests?

Regarding "interesting sites", what are you interested in?
If you enjoy museums, the Auckland War Memorial Museum, in the 75-hectare Auckland Domain park, has outstanding Maori and Oceania collections, and many other exhibitions worth viewing. The Maori galleries contain "the largest and most significant collection of Māori treasures in the world".
Home - Auckland War Memorial Museum
Auckland Domain
If you enjoy visual arts, you'd probably enjoy the Auckland Art Gallery, in the CBD.
https://www.aucklandartgallery.com/
You might find the Maritime Museum, at Viaduct Harbour, interesting. Auckland has been nicknamed the "City of Sails", due to the popularity of sailing, and hosted the America's Cup. Evidence strongly supports the belief that Polynesians were first people to arrive in New Zealand around 1250–1300 AD, coming from East Polynesia in canoes. Dutch explorer Abel Tasman "discovered" New Zealand when he sailed into Wharewharangi Bay, near Wainui Inlet to the north of what is now Abel Tasman National Park, in 1642, "but after a bloody encounter with Māori in Golden Bay, he left without going ashore." Until the 1940s, when NZ's commercial air industry started to take off (Australian aviator Charles Kingsford Smith made the first successful Trans-Tasman flight in 1928), pretty much everyone had to journey to NZ by sea. I've met many immigrants who moved to NZ in the 1960s from the UK, arriving here by ship. So you can see New Zealanders have a strong connection to, and dependence on, the sea.
https://www.maritimemuseum.co.nz/about-collection

You'll probably want to walk around Auckland's downtown waterfront (Viaduct Harbour, Wynyard Quarter, Princes Wharf, Quay Street, Queens Wharf and the Ferry Building).
https://www.heartofthecity.co.nz/all...and-waterfront
Mission Bay is also nice and has the best views of Rangitoto Island from land (in my humble opinion). I'd say it's about 6 or 7 km from Viaduct Harbor. I believe Kelly Tarlton's popular SeaLife Aquarium is over that way (sorry, I've not been there yet, though I've been to some of his other aquariums and loved them).
https://www.kellytarltons.co.nz/

If you enjoy wineries and great views, you might want to visit pretty Waiheke Island in Auckland's Hauraki Gulf. After arriving by ferry from downtown Auckland (40 minute journey), you can take a tour or get around the island by local bus:
Waiheke Island of Wine
https://www.fullers.co.nz/destinations/waiheke-island/
Volcanic Rangitoto Island, also in Hauraki Gulf, is a local icon. It's uninhabited, populated by native birds, traversed by walking tracks, and has splendid views from its summit. From downtown Auckland, the ferry takes 25 minutes to get to Rangitoto. You can walk around on your own or take the Volcanic Explorer.
Rangitoto Island: Places to go in Auckland
https://www.fullers.co.nz/destinatio...gitoto-island/
https://www.fullers.co.nz/experience...explorer-tour/
More Hauraki Gulf trips on this page:
https://www.fullers.co.nz/destinations/

Great Sights is one of the many companies offering one-day tour around Auckland and beyond.
https://www.greatsights.co.nz/find-a...from-auckland/

Tripplanner001, I was on your same wavelength!

I can't beat Diamantina's reply as she has covered everything. April 25 if you are here then is Anzac Day - a public holiday to celebrate WWI. Shops are closed until 1 pm and most people have the day off but not those in retail.