Unlike other countries, the peak competition for basketball talent resides in regional clubs that are partly state sponsored, not in the private school system.
There are good private schools with quality basketball programs, but they don't play all year round and the pathway to develop promising players is less developed than offered by the regional clubs. NSW state teams are drawn from regional clubs, not school teams. So - in Sydney's north have a look at Manly, Hills and Hornsby. Avoid Norths just now. (Great club, just going through some issues right now with venues and coaching). Closer to the CBD, Sydney Comets. In the south west, Bankstown.
Certainly private schools can offer an extra layer of quality coaching and playing opportunities which has proven useful recently with many comps shutdown due to Covid. In the north have a look at Redlands at Cremorne, St Lukes and St Augustines. Closer to town look at Scots. The other thing to keep in mind is whether you want your son to undertake the IB rather than the HSC. Here I recommend Redlands again.