Can you please prapose any ather place after the caves ? Except Blue mountains ?
Without knowing where else you're going to or how much time you have, it might be a bit difficult for others to make recommendations. Suggest posting your current itinerary by day - then others can help fill in the blank(s).
What interests you? How are you travelling?
Kanangara-Boyd National Park is not far, for bush-walking and canyoning. I wouldn't be canyoning at this time of year.
Even further...the Big Merino, at Goulburn.
You'll need a car.