By train
Cityrail trains stop at Blackheath Station every two hours off-peak and weekends, and more frequently at peak times. An adult return ticket from Sydney's Central Station to Blackheath is $19 for an off-peak return, or $27 if leaving before 9AM.
The station is located near the main shops and gives good access to the town centre. A shuttle operates over the road from the station. Govett's leap is around 3km from the station, and Evan's lookout is further. So, best to have a plan worked out if you are hoping to tour the attractions an vistas that the area is famous for.
By car
Blackheath is on the Great Western Highway, after Medlow Bath and is quite hard to miss. It takes approximately 1.5 to 2 hours from Sydney, depending on which road you take, and the traffic conditions.