Another governor who didn’t live in the official residence: Illinois’ Rod Blagojevich. Blago declined to move his family from Chicago to Springfield (the state capitol), and rarely used his offices in Springfield at all, preferring to operate out of his house, or offices in a state office building in downtown Chicago.
His motorcades frequently disrupted traffic in the city…and, as we learned during his corruption trials, it appears that staying in Chicago was, at least in part, a way for him to avoid actually doing any actual gubernatorial work.
Minnesota has a Governor’s Residence, but our current Governor is the first one in 15-20 years or so to actually live in it. It’s about 3½ miles from the State Capitol, where there is a sizable office for the Governor.
But currently, the Governor is operating out of the Residence, since he is recovering at home from back surgery.
The Prime Minister has his/her own 737. The flight from Sydney to Canberra (especially for a VIP aircraft) is barely more than 30 minutes and Canberra airport is only 15 minutes from Parliament House, so the commute isn’t so bad. To be fair, the Lodge (the PM’s Canberra residence) isn’t a great house (especially compared with Kirribilli House) and there has been a lot of talk over the years about renovating or replacing it.
Julia Gillard also decided not to move into the Lodge after she assumed the PM role until she won the subsequent election. This caused all sorts of headaches for the security people, who had to secure a non-descript flat/apartment. I can only imagine that a US President trying to live in a normal residence would cause an order of magnitude more problems.
Funnily enough for quite a bit of December the entrance to the Lodge was competely blocked off (I live in the same suburb, Deakin, and pass it nearly every day). They seemed to be doing some work on the place. Parliament doesn’t sit in December so Julia would have been wherever her “normal” place of residence is. Melbourne, presumably, since that’s where her seat (Lalor) is based.