Grillmarkaðurinn (the Grill Market) is a long-running upmarket restaurant in a corner building just off Lækjargata, with a downstairs dining room of wood, leather and warm lamps. The menu leans on Icelandic produce — minke whale, char, lamb fillet — much of it cooked over the open Josper grill that gives the place its name.
Mains around 6,500–9,500 ISK; their signature is a series of small "Icelandic experience" tasting plates that work well for a table sharing.