Tucked away in a little shopping arcade near one of the main shopping streets, this restaurant is central but a bit hard to find. However, it's worth seeking out if you're a vegetarian, as it serves excellent food which is filling and freshly made. I've been here several times in 2010 and 2012, and have been impressed by the quality of food on each of my visits. There is usually a small selection of main dishes, each of which comes with salad, bread and pure Icelandic tap water. Dishes cost about 1,500-1,700ISK each, which is good value by Reykjavic standards.
Graenn Kostur is more of a cafe-style place than a restaurant, and while it's certainly clean and comfortable, it's not the sort of place you'd want to linger for a long romantic dinner - it's best suited for those looking for a quick meal. Also, as has been pointed out by others, the service, though not unpleasant, is a little aloof. However, if you come to Graenn Kostur for the food rather than the atmosphere, you certainly won't be disappointed.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.