100's of walking trails in the blue mountains. How much time do you have? There is everything from 1hr walks to 5 day treks. Jenolan caves would be my pick if you have never been there. Easy access, food accomodation etc, with plenty of choices in cave tours.
In katoomba you could do something like, walk down from 3 sisters to the valley and up the other side via the railway. Heaps of choices in that area and will depend on fitness and time.
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