Auckland is a metropolitan sprawl of many neighbourhoods - some worth venturing into, some not!  Around the city:

PONSONBY - Is the cafe/latte/arty/bohemian/gay part of Auckland - located about 5 minutes drive west of the CBD.  This area has interesting boutique shopping and has (probably) the highest concentration of cafes and restaurants in Auckland, so is a good place for dining.  The easiest way to get to Ponsonby from the CBD is via the inner Link bus (exit stop 7212), which stops at Britomart, up Queen Street as far as Victoria Street, and outside the Casino. Exit at this stop, walk across the road and meet beside the Western Park wooden sign and treat yourself to the 10am Edgy Auckland

NEWMARKET - the main shopping area, this suburb has everything from local designers and brands (including Karen Walker, The Stockroom, Taylor Boutique, and RUBY) to big multinational brands such as Country Road and Witchery.  Again, access is easy on the Link bus (in the opposite direction from Ponsonby), and via train from Britomart. A train ticket from Britomart to Newmarket is $2.50 if paying during each ride, or cheaper if you purchase a HOP card which can be used on all public transport.

DEVONPORT - a quaint seaside suburb on the North Shore, this suburb has a village feel.  Devonport is a quick 10 minute ferry trip from the Downtown Ferry Building, or in a hire car take the first right after travelling north over the harbour bridge.

MT EDEN - good to get up high and see the view from the top of  the mountain, then head into the 'village' and visit one of the 5 or 6 cafes or over a dozen restaurants. Mt Eden also has a couple of good bars (De Post and The Horse and Trapp) which do food as well. There are boutiquey shops and a couple of interesting book stores (cook the books and the womens book shop). Its easy to get the bus to Mt Eden from Britomart at the bottom of Queen Street. You can also get a bus from Mt Eden to Newmarket and St Lukes.

ST LUKES - One of Aucklands big malls, St Lukes is probably the most established, having been around in various forms for many many years, it now includes a movie theatre, bars, restaurants, FoodTown supermarket, K mart, and all the major clothing labels, plus some only found in St Lukes. If you are into shopping and its raining, you could do worse than a few hours mooching about in the mall. It has a massive carpark (much needed because it can get very busy) There is also a library next door and a football field.