TES II: Daggerfall - Part 03 - The Missing Prince
A letter arrives from Prince Lhotun of Sentinel, who claims to have some information about the late King Lysandus. Once Bumblebus arrives, Lhotun syas he'll tell him what he knows if Bumblebus can help him find out the truth about his missing brother.
A while after his inquiry, Bumblebus is given a note from a stranger who sends him somewhere in Sentinel to find his answer.
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This quest randomly selects a dungeon for the objective to reside in, and may even randomly drop it in the dungeon (although I don't know if the latter is true or not), so these types of quests will not go quite as smoothly as others in the series.