For Lincoln's rock, if you want to get there by public transport, it will involve a very long walk from the highway. So in theory, it's possible, but in practice, nobody would do it.
If you don't mind the excessive driving, you can have a day trip west to the Blue Mountains, south along the coast to Kiama, north to Central Coast, a separate day also north to the Hunter Valley for wine, and south west to Southern Highlands. If you're insanely energetic, you can even fit in Canberra in a day trip. All of those trips will take care of most of your time in Sydney.