Hi all, me and my wife are experiencing the same situation, being arrived 3 weeks ago here in Adelaide with no jobs.
The tips I can give to the OP are:
1st: search (on internet or wherever) the addresses and/or the telephone numbers of the companies you'd like to send your resume. Call them before, and then send your resume attached to a customized cover letter that clearly refers to your previous contact. This can make the difference between a considered resume and a discarded one.
2nd: before choosing your fina location try to secure a job during the short term rental, if you can have one. If it isn't possible, try to choose a suburb placed in the middle of the urban area, but consider that if you're somewhere on the hills you'll reach both northern suburbs or southern one more easily than starting from a trafficated central part of the city, as i.e.Mile End or Unley. That's because starting from a peripheral suburb you'll face the traffic only in the last part of your journey to work.