Hi John,
There is another option in the Blue Mountains.
Leura Golf Club is a short taxi ride from Leura train station. I've used a scope on their course one night I stayed up there. Did it on the sly, but a lovely place.
Drop them an email explaining your intentions. They may be able to accommodate you on one of their fairways.
Like Wavy said, it can get cold up there, so go prepared.