Originally Posted by
kirkwoodj
Train runs almost right under Hilton, loops around to Circular Quay, and has lift(elevator) access. Little hike to Opera House from there. Taxi wouldn't be too much to any of the Sydney attractions you listed, depending on traffic. Tower is just over a block away. Blue Mountains--would consider a touring coach (bus) for your needs. All the best, enjoy my hometown!
Uber is also available in Australia; it's usually a bit less expensive than a taxi. Blue mountains are a ways out of town, so consider a train and then a tour or Uber from there if you don't want to book a tour from Sydney, or a car hire.