Note! This quest is optional, but its completion can bring you closer to unlocking next major Companions quest.
Possible quest givers are Vilkas or Skjor. After you agree to complete the task, you'll be asked to retrieve stolen family heirloom, kept by bandits in the randomly chosen location in the game world. Leave Whiterun and travel to the place marked by the game, which can be an encampment or underground bandits' hideout. Eliminate all local opponents and then look for family heirloom, which probably is hidden in one of the chests (screen above). You can now return to quest giver and collect your reward in gold.