How "in or near" do you want - they are two different parameters given the size of metro Auckland. Baches are very casual holiday homes - and would be more than an hour from Auckland City eg Whangaparoa Peninsula. Apartments would be more likely to be in inner beach-side suburbs like Mission Bay,
Kohimaramara, Devonport, Takapuna etc. For only one week why not choose a motel - since August is off season you should get very good rates for a week and some motels have 2 bedroomed units (they may call them "family units"

.
Again I'd try Takapuna or Devonport.