Public Transport in Canberra looks good but can be quite difficult. We wanted to Visit Telstra Tower but without a car it was almost impossible. Either a 1 hour uphill walk or a $20 return taxi fare. No buses run to the Black Mountain lookout. National parks are also very poorly serviced by Public transport.
Fun Alternatives: Why not try visiting Mt Ainslee, there is a walking track from the War Memorial or you can cycle up with the free cycles at the YHA!
Great view and no charge