Sydney for 10 days?

hey peeps, i'm going to Sydney to 10 days in September. I want to get a true Australian experience. Want to see the city and the Blue Mountains. But, where can I see a kangaroo Crossing sign?? Im renting a car and planning to do some driving to the outskirts...is it possible to see one of these signs? Also, what are some MUST SEE MUST DO'S. I wanna make our trip a very memorable one! Thanks!