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

The heroes are 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 heroes must talk to various innkeepers, merchants, and other NPCs in hopes of learning about the subject’s movements. You say he was on his way to Dunsdale? 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 game like Scotland Yard or Fury of Dracula. Of course, your version should be simplified, since the game isn’t limited to a board. Roll 1d20 against a difficulty you set depending on the likelihood the NPC has heard of the subject and can direct the heroes to someone with some knowledge of his or her movements. Some of these might be willing while others are quite cagey. Reaction checks, charms, and cold, hard cash might draw out a solid lead (gain a bonus to the questioning roll) to the subject’s next move, especially when the heroes know they’re talking to someone who actually interacted with the subject.

• The heroes are tracking the merchant Edlar Folding—who moves from town to town, buying and selling goods—to deliver an important message from a business partner about a shipment. 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 shipment message could be a lead for the heroes’ next adventure; perhaps it was seized or run aground on an island.)
• 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 a 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. What the heroes won’t know—unless they’re very careful—is that rogues are tracking them, so when they find Wenda, there’s sure to be a fight.
• 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 identifiable by the scars from a fire that burned one ear, something he sometimes covers.
• The heroes are tracking Alandis Helver, a sorceress who plans to charm a dragon and get it to destroy a city. She has gathered certain things necessary to create the potion she’ll need but needs to go to Alavar city to get an aboleth’s heart, then Ventir to get dragon blood, then deliver them to a coven of witches in the wildwood to create the brew. If successful, she’ll take it to the dragon’s lair on King’s Peak mountain, at which point the game is lost (not to mention the city). She uses a hat of disguise but can be recognized by her dragon tattoo and her thuggish bodyguards.