In reply to tompickersgill: as many people have suggested, Arapiles is your best bet. Campsite to closest rock is probably 100m, and there's usually people camped semi-permanently all year. Not much in the way of sport climbing though, primarily trad and there are a lot of boulders about. Probably best to avoid it during the Australian summer... I was in the Grampians (about 1hr from Arapiles) after Xmas last year and the temperatures got above 35C.
Re: Sydney + Blue Mountains, though I live here, I'm not sure it's the best destination to camp and just climb. Arapiles seems a better fit for that. If you wanted to work as well, Sydney is a good location. Enough small crags and bouldering spots dotted around the city, and the Blue Mountains and Nowra within a few hours drive.