Dyri is in the Dwarven tavern, underneath Thorin's Hall in the mine tunnel.
To find the tavern, there are two entrances to the mine tunnel, east and west off the central hall. They show on your map, but you may not twig to what they are unless you're looking at them (I didn't).
The east entrance is probably easiest to find -- as you go down the east stairs into the Maker's Hall, look for the passage on your left, right beside the stairs. Another way to find the passage is to head north-west from the NPC Egil Oldbeard, who stands near the bottom of the stairway.
The tunnel curves around to the west and comes out on the other side of the central hall. If you're looking for the west entrance, look to your right as you walk toward the NPC Kimbur Green-Tree.