The Crown and Lion

(1) Once inside the Crown and Lion, speak with the innkeeper in the common room. Ask him if he's seen Kristoff, and then tell him that you're Kristoff's commanding officer to get the key to Kristoff's room. The dwarven bartender to the innkeeper's left sells goods and holds many secrets regarding the smugglers in town, if you choose to do some of the Amaranthine side quests.

You can also question Sorcha, the barmaid up the stairs toward Kristoff's room, and she'll reveal some insight about Kristoff's general mannerisms.

(2) Use the key the innkeeper gave you and open Kristoff's room. Pick up Kristoff's Mementos, a gift item, in the chest to your right, and gain Kristoff's Journal codex entry from the book on the table.

The chest by the bed holds the Spirit Cord amulet (+3 dexterity, +3 cunning, +15% nature resistance, +5% spirit resistance) and A Letter from Aura codex entry. When you interact with the Map of Ferelden on the back wall, the Blackmarsh location opens up on the world map. You can now follow Kristoff to the marsh and see where his pursuit of the new darkspawn led.