Woolwich has a public wharf,
There is one near the Dawn Fraser Bath below Fitzroy Ave. Balmain and one at Callan park if you fit under Iron Cove Bridge. This last one is the most sheltered one.
lf all else fails, Five Dock Bay is usually good, anchor or pick up an unused mooring.
One should be careful going up at wharfs, if there is any wash from a stinky, the hull is going to be bashed against the wharf. When this happens while one is up the mast, bad things might happen. l am doing it on my mooring early mornings or late afternoons despite the possible pendulum effect keeping one eye on the water at all times.
Good luck!