Flatting in an apartment in the city centre or sharehouses in areas surrounding the city would be a good option. Flatting would give you more flexibility on the period of your stay compared to renting an apartment on your own. (Also less lonely!)
Trademe Flatmates is a good place to find sharehouses/flats.
If you prefer to have a place on your own or you have a friend you want to find accommodation with, Trademe also has lots of rental listings.
There are quite a few apartments on Symonds Street (which is where the Univ of Auckland and AUT are). I would look for apartments with addresses between 25 to 120 Symonds St. Or on Anzac St (which is connected to Symonds St).
Suburbs like Ponsonby, Mt Eden, Parnell have regular buses to uni and are nice areas with lots of restaurants and cafes. City Centre would be ideal if you want to be in walking-distance to uni but it might cost a little more or the size of your room may be smaller. Any of the areas within the blue circle would be okay:
Just as a side note, personally I would not live on K-rd (Karangahape Rd). It is an interesting area during the day, but not the best place to be at night especially if you need to study or sleep.
Another option is finding a "Homestay" family. This would usually be in a residential house so it would normally be in areas outside the blue circle. Homestays may provide breakfast and dinner, and the rent you pay usually includes all expenses like electricity, water, gas..etc. It may take around 20~30minutes to get to Uni on public transport. (eg. From suburbs like Grey Lynn, Mt Albert, Epsom, Remuera)
If you are thinking of homestays as an option, the North Shore (over the bridge) may also be a good option. It is a less busy area with families with young children/teens. It may be cheaper and takes around the same amount of time to get to the city centre (20~30min) as there are regular express buses. Takapuna, Forrest Hill, or Milford would be ideal suburbs in this case.
There is also the option of hostels. Note that you will be sharing the kitchen, fridge, bathroom...etc with others.
Universities also have their own halls of residence. They usually provide three meals per day. Check out your host university's website for more information.
When you are looking online for accommodation, try checking "Street view" on Google Maps. You can get a feel for what kind of area it is. Also, Auckland has lots of hills so you can check out if you are going to have to climb lots of hills to get to your apartment/flat.