The Blue Mountains are one of my most favourite places in the world. I grew up in the town (suburb) at the base of the mountains and I lived on the Nepean River in Penrith. I recommend that you go to Katoomba and check out the three sisters. Also at the main strip of Katoomba should be the Paragon Cafe which is worth a visit for their home-made chocolates.
There are a number short easy bushwalks you could do around Katoomba and Wentworth Falls. The Hydro Majestic Hotel (at Leura) was the base of the American Forces during WW2 and is a beautiful old art-deco building and has stellar views out across the Jamieson Valley. Of course, Vipassana Meditation Centre Blackheath (Dhammabhumi) is located on Station Road, Blackheath and is worth a visit if they are not holding a course. Also at Blackheath and across the rail-line and a couple of km to the north is the famous Govett's Leap. Keep in mind that if you are going to the top of the Blue Mountains this time of year it can get very cold and snows there sometimes during winter.
I'll get back to with some other suggestions of places to visit on the way up to, and around Sydney, later today - as my break's about to end.
“No lists of things to be done. The day providential to itself. The hour. There is no later. This is later. All things of grace and beauty such that one holds them to one's heart have a common provenance in pain. Their birth in grief and ashes.”
- Cormac McCarthy, The Road
Learn this from the waters:
in mountain clefts and chasms,
loud gush the streamlets,
but great rivers flow silently.
- Sutta Nipata 3.725Compassionate Hands Foundation
(Buddhist aid in Myanmar) • Buddhist Global Relief