In the past, U.S. Presidents and their staffs traditionally stayed at U.S. Embassies. But Obama is too good for that apparently.
There’s no US Embassy in Brisbane - it’s a state capital and the Embassy is in the national capital, Canberra. There isn’t even a US Consulate in Brisbane. Not saying the President would have taken that option even if it had been available, but it isn’t even an option in this case - the nearest US Diplomatic Mission is the Sydney Consulate and that’s about 450 miles away.
http://www.americanembassyinformation.com/brisbane-australia.html
No embassy in Brisbane.
Also, when presidents are out campaigning, they stay at Security-approved hotels in US cities. I know that at the St. Francis in San Francisco is one of those.