For consistency, I'll replace 'the the' in the following ways:
put '(sic)' afterwards if it's a mistake in the game
(...) in the The Quest Name -> (...) in The Quest Name, if 'The Quest Name' is the full name of the quest
(...) in the The Imperial City -> (...) in the Imperial City, if it's a normal place or person's name
(...) in the The Flowing Bowl -> (...) in The Flowing Bowl, if the place's name is somewhat officially using the article, as in 'The Flowing Bowl', the full name of the inn (and here, 'AnvilTheFlowingBowl' console code)
(...) in the The Book Title -> (...) in The Book Title (if the title does use 'The')
(...) on the the other web site -> on the other web site
(...) in the the -> (...) in the, in other instances