I did hour building in both the US and Oz. I far preferred Oz, where I did around 70 hrs flying out of Bankstown in Sydney. In the US I flew out of Long Beach in California. I used Schofields Flying Club in Oz, flying Piper Arrows.
In Oz, the process of getting a Special Pilots Licence to fly on your UK licence is protracted and lengthy, and you need to start thinking about it long before you go. Search the Oz CASA web site for forms and info.