Here's a quick list of some solid "nicer" options in Auckland:
Amano - good for breakfast, brunch or lunch. In the Britomart area of the CBD. Upper-mid tier pricing. Locally famous for just being solid all day food. An alternative to this is a place called Ortolana, not far from there.
Alma - Spanish style food. Located not far from Britomart. They have a tomato martini style cocktail that is excellent. Highly recommend.
Ahi - more on the fine dining end of things, but not overly formal. NZ local ingredient centric dishes. Located at Commercial Bay. Good views too.
Mr Morris - another higher end option that I really enjoy every time I go. Unique menu.
The Grove - local institution. White tablecloth type place, so it isn't cheap. However, a top tier dining experience. Actually owned by an American - really nice guy.
Hello Beasty - in the Viaduct area, good spot if you like Asian fusion.
Kingi - good local seafood, if you're into that.
There are some great food & wine experiences if you take the 40 minute ferry from the CBD to Waiheke Island. Good day trip.
A cool rooftop bar just opened up at One Queen (where the Intercontinental is, connected to Commercial Bay)