Some adventurer used to store his loot under a loose board in the stable to the north next to some strange note on the wall. He might have forgotten something when he left.
Tom mentions an adventurer leaving a doublet in his cellar before leaving for the mainland.
You have to go to the stables north from Tom's shop, go down the ladder and light your torch. Kill the two rats possibly spawned there, and then "Use" the ground straight left from the sewer's entrance to get the Doublet, and complete this quest.