Go out onto the pier and talk to the fisherman. Leave the jail and walk towards the waterfront on your right. Before leaving take the Manilla and Gorilla envelopes from the shelf and open them.
Then give the bone to Walt the dog, pick up the key, and unlock your cell. Use the stick on the leg bone of the skeleton in the cell next to you. Lift the rock-hard mattress and pick up the stick from the frame underneath. This area has great music but you really should be going. Guybrush is invited to meet the Governor, but not in a good way.