The City sauna would have been Kings Steam, it was located on King Street in Sydney, it later relocated to Oxford Street, as far as I know there the rooms were not numbered, Harbour City Bears held a Gorillas in The Mist night at Kings Steam for bears, chubby guys and their admirers. Harbour City Bears have a lot of social events during the year.
There was also another sauna called KKK aka Ken’s Karate Klasses in the Sydney suburb of Kensington, having not lived in Sydney for 23 years I don’t know if either of these saunas are still in existence.