I stayed at the HI hostel in the rocks area. While this is more pricey than others I’ve stayed at around Queen Street downtown, the view from the balcony overlooking Sydney harbor and opera house was worth the extra price; also this wasn't a long visit. Just down the hill is the waterfront area with ferries to many parts of the city. Take one to the area near the entrance of the harbor for scenic parks and many walks to choose from. The harbor is amazingly beautiful and is said to be one of the best places in the world to sail in. There were definitely no shortages of sailboats out that day and I even one of the old school tall ships. Cafes, museums, expensive and cheap eats… Sydney has it all, including the nightlife.
I decided to spend the extra cash to see a show in the famous opera house, which is highly recommended. The ticket price usually starts not much higher than the price of a tour and you get a show out of it; the Sydney Orchestra in my case. They even release tickets at a more discounted price around one hour after the show starts for all the will call tickets that went uncollected. Even when traveling on a budget, I think it’s important to spend the extra cash to experience memorable things like this. I attended a show there years ago when I was traveling for months in Australia and its still one of my best memories from that trip. It was great to get back and see another!
I even got out to a boat show to round off the trip in the suburbs north of the city. To me sailing is similar to traveling since people can do it on a budget or spend crazy amount of money; it's a way of life for some. Of course a person can travel to distant places while sailing, which is the best kind in my opinion... but that will have to wait for another trip.