Are there any private schools in the Blackheath area?

Blue Mountains Grammar School in Wentworth Falls is the largest Private School in the Upper Blue Mountains. They cater for K-12. They also have various scholarships available.

There is the Blue Mountains Christian School in Blackheath. It is K-12.
There is also Blue Mountains Grammar in Wentworth Falls which is about 20 minutes away.
Korowal School is in Hazelbrook which is about 30 minutes away.
There are Catholic Schools in Lithgow, Katoomba and Winmalee.