You got your wires crossed. The freebie is on top of the Thompsons Point climbing area, but is real bush camping well away from the town with absolutely no amenities. There have been no car break ins for a while (touch wood) so don't worry bout that. The animal park/ski park are $10 a night and directly over the river from thommos and have all amenities - and the canoes require a $50 returnable deposit in case it goes missing which most ppl dont realize.
The other option is the showground. They lock the gates at 9 to keep the hoons out and its free. Only prob is you gotta pack your tent up every mornin and put it down again every night.
New Nowra is about a 30 min drive from the Nowra town where all the other climbing is. If youre only coming for a coupla weeks and dirtbagging - forget it its not worth it.
By the way - the weather is shit here right now, and not much better up the bluies as far as I hear.