Blue Mountains
Since you've mentioned you like walking, a trip to the Blue Mountains from Sydney is worth it. Can be done done as a day trip, but would be worthwhile staying at least one night, as a day trip would be rushed (it's about 1 hr 45 min. drive from Sydney each way). Katoomba is the central town in the Blue Mountains, with many places to stay. You can also catch the train there from Sydney, which takes about two hours and is very cheap. The only problem with that is it's not that easy to get around without a car. There are other nice towns in the Blue Mountains, but they are smaller and more remote. I recommend the National Pass (national pass.com.au) - a great walk!

In general, you've picked some great things to do/see, some of which I haven't done but would love to (train).