One of the best cheapest things to do in Sydney is to take the Manly Ferry from Circular Quay especially if it's a fine day. It takes 45 minutes one way, and is much better than booking any dinner cruise. Once you get to Manly, there's not that much to see/do except maybe walk to the beach, but the beach at Bondi is much nicer, so I generally turn around straight away and get on the next ferry back.
On the contrary, just a 5 minute walk through the open mall you will reach Manly beach which may be a great few hours if the weather is warm. Manly is a beachside suburb of Sydney. Bondi beach is nicer, more famous, buzzier and prob more gay(at one end anyway). Manly is still worth it!
Also, with regard to the Blue Mountains..it's well worth the day trip. There are nice day coach tours or you can catch a nice train there for the day if you dont want to drive..quite a lazy day. You also have the option of Jenolan Caves - limestone formed caves with some of the most beautiful shapes and forms you will ever see , naturally formed over thousands of years in rock face.
CJ