In his home town of Sydney. The office of the PM has long enjoyed a Sydney residence, Kirribilli House. But Howard is the first PM not to live at The Lodge in Canberra since the capital was founded in 1927. (Melbourne was the de facto capital before that.)
And even Sydney-based conservatives don't like it: http://www.theage.com.au/handheld/articles/2003/01/20/1042911326471.htm