I will stay in central Sydney for a few days and would like to do some climbing one evening. What would be the closest (or most convenient to get to without a car) indoor climbing wall from Centre Point Tower? (it obviously needs to be accessible by general public)
There's two close to that there I'm aware of.
Mountain Designs City Crag. Located within the Mountain Designs store (go right to the back and its on the left) at 499 Kent st. Sydney (about 2 blocks from Centrepoint). This has closed and re-opened at least a few times over the past few years, so it'd be worth calling first to see if they are actually still in operation.
Virgin Active Health Club Pitt st Mall. Sydney. I've never been here, so I've got no idea what their access rules are (eg, whether you need a membership, or if you can just do a single visit)
If you're willing to go a few stops on a train there's a few other options :
Sydney Indoor Climbing Gym at St Peters (Unit 4C/1-7 Unwins Bridge Road) which is probably the largest in Sydney, and
Indoor Rock Climbing Gym Sydney at St Leonards (Unit 4/12 Frederick St)