The best time to go to the museum are 11am and 2pm. You will be able to see the Maori performance there. If I am you, I will go to the museum before lunch, then walk down to Parnel for lunch. After that, you can go to the city CBD and have a good walk around the wharf.
Auckland also have good "yumcha" too.
Some restaurants do good seafood but they are quite expensive. There is a good fish and chips shop at Mission bay. (10 minutes from Auckland CBD )
If you go to Mission Bay, you can try to take your nephew to rollerblade if the weather's good.
If i am in Auckland that time, you can try to contact me / if I am "hima" at that time because I am thinking of going up North for a beach x'mas.
It depends on what you like.
Devonport is a nice place to visit. Like what Mayumi said, the supermarket may be a fun place for you to spend some time on. But I think you can go to supermarket at night time as the supermarket in Auckland central open for 24 hours ^_^. Mt Eden is ok too and it would not take too much time to look at.. may be an hour.
Museum , Devonport and Mt Eden would take you a whole day. ^_^