Queen Street's worth a walk down (The part from the IMAX northward). Many shops and an inordinate quantity of Starbucks. About halfway down you'll catch a glimpse of the quaint little Vulcan Street, it's steep, inhabited by many little boutique stores, and has a Belgium Beer Bar (I wish Adelaide had one.. oh wait..
Take the kids a few minutes South for a day trip to the Mt Eden Domain, it's an old Maori stronghold on the top of a ancient volcano. Auckland's spattered with such outcrops, most of them serve as parks. Mt Eden has a visitor's centre with a bit of history and depending on the day there's often people dressed in victorian garb to recount it. Make sure you're wearing your walking shoes, it's a big hike to just circle the mount, let alone walk up to its peak.
Back on Queen street, you might want to visit our overlords at the original Sky City and enjoy a silver service meal on the revoltin' restaurant. You can even jump off the tower if you want (on a braking zip line - what spoil sports). It can be a little unnerving seeing people plummet past the restaurant's windows while eating.
The marina part of Freeman's bay is pretty, there's a maritime museum and a lot of restaurants. The very end of Queen street is a pedestrian mall with some attractions.
Just don't hang around Auckland's CBD after dark, that's when all the thugs come out and cause trouble. Especially near the corner of Queen and Customs streets. Auckland's the only city I know where the local police are boosted by security guards who patrol an entire area.
Driving in the CBD is MAD! Don't do it unless you have to. The roads are narrow and curvy, no one drives to the conditions, they go about three times what they should. They do have a good bus system, but make sure you have bought enough fare, as they charge per section, and the drivers somehow keep track of exactly where each passenger must get off. And they enforce it with the kind of respect that only huge Polynesian guys can command. One bus I was on, the driver stopped and pointed at a woman near the back and said "YOU! your ticket has expired, get off or buy another!" They stared at each other for a few minutes before she broke eye contact and got off.
Also don't worry if the bus you're on scrapes up against a parked car and just keeps driving. It happened twice while I was there.
I was only there for four days and I found plenty to occupy myself.
Exit on the right in the direction of travel.