Hey Briskx,
I'm living in Sydney, in the inner west about a 15 minute bus ride from the CBD. I haven't found a room with American-style tables but I honestly haven't looked for one very hard, and as has already been said the easiest and cheapest way to keep occupied here is to join an RSL that has snooker tables, as it'll only cost 5 bucks or so for the yearly membership and the tables are free to play on. They usually do handicapped weekend tournaments for snooker and English billiards (I lucked into a win on Saturday for the billiards!) for money or meat tray prizes and it's a fun environment and a great way to play locals.
PM me and I'll get your number.
There are snooker tables in the CBD , I think, but they're in the only expensive, exclusive RSL around, so you're probably better off playing in Drummoyne in my neck of the woods where the tables are free. I've also been sourcing some carom tables in the Korean and Vietnamese neighborhoods, if that interests you. I miss 3 cushion the most and want to get back to playing.
Any other AZers out there feel free to join in as well.