We lived in New Brighton for about 4 months back in "07. Had our car window broken and 2 other break ins on our cars. Plus outside of our flat vandalised. And, we kept to our selves. Our neighbour was a 30 something stripper with a 16 year old boy friend, they had plenty of fights and loud arguments near our flat. New Brighton is next to Aranui, so some of the crims from Aranui do their dirt in New Brighton.
The beach, library and shops are nice. Basically a nice place to visit during the day but you don't want to live there. We paid $$ to get out of our lease and moved to Rolleston
Most of the flats are old and uninsulated, and unlike the US and Canada, landlords in NZ are not required to provide a source of heat. The plug in electric heaters only heat small areas, you freeze your bum off and pay a fortune in electricity.
The other areas mentioned are nice, you may also want to consider Papanui. When searching for a rental be sure to ask about insulation and source of heating.