hi AnxiouslyExcited and everyone else. A good friend just moved to Auckland and here is the summary that I put together for her - it's not quite "Where to live in Auckland" but I think that it is a reasonable summary for starters.
lollystix makes an excellent point, living in Auckland is all about school zones, so you need to take that into account wherever you go.
So here goes...
Auckland can be divided up into 5 main-ish regions.. Central, Eastern Bays (part of central really), North Shore, West Auckland and East Auckland.
Central, obviously, is closest to the CBD. The 'trendy' inner city suburbs are Ponsonby and Freemans Bay (also Grey Lynn, Herne Bay and St Marys Bay). Very cool but an affordable place would likely be quite small and probably no parking.
Parnell is on the other side of the city. Great for shops and stuff but very expensive.
Still very central is Mt Eden. The Mt Eden village is lovely although maybe not quite as trendy as Ponsonby. Still quite exey.
An older and posher bit of Auckland is Remuera - people associate it with snobbery as the most expensive houses in NZ are here, but it is a very nice suburb.
Eastern Bays - Mission Bay, Kohimarama and St Heliers Bay. Very lovely and have a beachy/villagey feel. Some places have lovely views of the harbour. Not quite as central and can be a pain to get to in peak hour as there is only one main road to and from the city.
East Auckland - I wouldn't bother about this unless your job is out this way. Nice but a bit far out. Can provide more info if required. Same with West Auckland really - there are some nice bits but I wouldn't live out there unless there was a reason. Cheap though, so you could probably get a mansion for $700 pw.
North Shore - I haven't lived there but DH is working over there at the moment. We are half considering moving over in a couple of years time as your money goes a bit further (when buying anyway). The main detraction from North Shore is the commute - the Auckland Harbour Bridge can be horrible in the mornings. Probably the nicest suburb is Devonport, but as you can see from a map it is quite isolated. Takapuna is central and popular. Lots of other suburbs on the north shore but I would start with those two.
We live in Mt Eden, albeit in a cheaper part not near the village...
Obviously there are lots of other suburbs, but this should give you a feel. The best website to get an idea of what is out there rent-wise is trademe.co.nz
Auckland is very green so you should have no trouble finding somewhere that is walking distance to a park, and all of the suburbs that I have mentioned have good access to shops.
Hope this helps.