I am not greatly familiar with Auckland, only been there a handful of times. My son lives in the CBD now attending the University of Auckland. He's home on break so I will ask him for his recommendations too.
The SkyTower is kind of cool. If you are an adrenaline junkie you can jump off of it. I prefer to stay inside and watch the jumpers come down. If you have the time and the weather is good, catch the ferry from the harbour by the CBD and spend an afternoon in Devonport. It is a nice place to just stroll around the shop and cafes.
There are many choices for restaurants in the CBD. I can't recall any by name, but we usually walk about and see what strikes our fancy on any given evening. You'll spend some coin as everything is expensive here. You do have a very favorable exchange rate working in your favor currently.
If you like red wine, look for a Central Otago pinot noir. Very nice!
Lastly, find a suitable pub to watch the rugby tonight if you get in. The Super 15 final has two NZ teams playing. My local team the Highlanders are going to win it.