The Walking Stick is found in the Laundry of Chinatown.
On Day 3, a Dragon uses it to hit the Manhunter unconscious when he enters, who then falls unconscious and kept in a locker room. He is then freed by a Slave he had helped earlier. Before escaping he takes the Walking Stick standing there.
He uses the Stick later to take the Ring from the neck of a Dragon's corpse hanging from the neon sign of Ghirardelli Square.