From Sydney Airport:
Contact Sydney City Shuttle from the domestic/international airport terminal (there is also a free phone you can use at the airport accommodation board, just ask information counter where it is). They will transport you directly to Asylum Sydney. Cost is AUD$12.
A train from the airport to Kings Cross costs approximately AUD$15 and requires changing trains at Central Station. We are a two-minute walk away from Kings Cross Station - use Victoria St. exit. We're located behind the Holiday Inn Potts Point.
Taxis are also available for A$30-40.