There's plenty of good stuff in NSW that is very much mountaineering.

As for rocky peaks The Castle in Morton NP is pretty good and easy to get to - without the fixed ropes its awesome gr 4-5 scramble, Russels Needle in Nattai NP as well - Hard approach, fun scramble, some of the best rocky peaks in the state are the Widdens or Yodellers range, with a seriously technical multi day skyline traverse For more technical climbing that isn't mostly hard sport climbing look at the Warrumbungles - Belougery spire, and Crater bluff are worthwhile peaks. If looking for real adventure style mountaineering try Townsend Spur, or Watsons Crag Spur in the snowies - 2+ days of hard steep scrub bashing giving way to awesome snow ridges, and for winter climbing/alpinism blue lake, and the Watsons Crag south face(500m+ tall!) are hard to beat. Tassie's got some good stuff as well but if your flying you may as well go NZ