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I'm in Zetland, all of those spots don't seem far. It felt weird cycling on the pavement but as you say, most people seemed cool with it. Might get a bell whilst I'm here, seems like a handy thing to have when you have to hop onto the pavement. I'm right next to the M1 so a lot of the roads near by are quite large/busy, need to get my bearings and I think I'll find ways around. I get what you're saying about drivers, some dude stopped right on top of a crossing when there was loads of space. Started giving grief when I cycled around, wasn't bad though. Not what I needed when my body was still working on uk time.
Where are you in Sydney? In and around the CBD there's bike lanes - So places like Randwick and Alexandria through to Surrey Hills, Paddington and the city centre have quite good routes. Even out over Anzac bridge to Balmain there's really good paths that allow you to explore the waterside around the area.
There's hills everywhere and even on smaller roads the traffic moves fast so you have to watch out for that. When I was there last people seemed to accept riding on the pavement when the roads were too crazy/busy.
I'm from Sydney and go back every year and have noticed great improvements but drivers attitudes are still the same. Riding up the coast from Manly to Bobbin Head or West head is a popular road cyclist route and drivers are generally are more accepting on those roads. Northern beaches in general has a lot more people on bikes.