Rather than a discreet problem like a single room in a dungeon, this is an adventure-scale predicament.

The company of heroes is tasked with tracking down a specific NPC. That character is known to be in the area and isn’t in hiding but is highly mobile. The company must talk to various innkeepers and other NPCs in hopes of learning about the subject’s movements. You say he was on his way to Dinsdale? Let’s hire a coach!

The subject has a specific task of his own, so he’ll go from one place to another to conduct his business and may well talk about it in each place. So the heroes can gradually learn about his purpose as well as his stated intentions and, by asking the right NPCs about where a person with such a purpose would need to go, guess at his next move and catch up with him.

This is essentially a hidden movement board game, like Scotland Yard or Fury of Dracula. Of course, your version should be simplified, since the game isn’t limited to a board.

• The heroes are tracking the halfling bard Wenda Loblolly. But she’s in danger from a noble who’s put a price on her head for song mocking him. Oblivious, she needs to get new strings for her lute in Hendel so she can play at an inn in Thorsby, after which she’ll take her pay to the halfling town of Trimpt to give some her her mother, Thessaly Loblolly, before journeying off the Scargaro city, at which point she and the game are lost. She’s easy to recognize and uses her name liberally.
• The heroes are tracking the merchant Edlar Folding, who moves from town to town, buying and selling goods. He starts with wool in Shepton, which he trades for grain in Wheaton, which he sells for gold in Minton, which he uses to buy linseed oil in Flaxton, which he will board a ship with to sell in a foreign land, at which point the game is lost. He’s nondescript but wears a distinctive light blue cloak and uses his name liberally.
• The heroes are tracking the outlaw Bodger Scox, who moves around in the local countryside from village to village and occasionally in a town. He robs a merchant on the road between Hirth village and Snazel town, buys arrows from a fletcher in Snazel, poaches a chicken in Fordsley village, robs a priest of his horse on the road between Fordsley and Ommer town, and spends the night in Ommer changing his appearance to ride out of the shire, at which point the game is lost. He uses fake names but is recognizable by the scars from a fire that burned one ear and the side of his face, something he sometimes covers.