Maybe you searched for Canberra City (suburb).
http://www.realestate.com.au/property-house-act-holt-118985271
http://www.realestate.com.au/property-house-act-bonner-119246211
http://www.realestate.com.au/property-house-act-dunlop-119044007...
I just noticed Goulburn mentioned in a 'hotspot' type thing in a new RE magazine, is that a coincidence? What do you mean by 'bargains under 350k'? You could still get a house in Canberra for around that, better job prospects.