Kaffi Hljomalind is one of the most vegan-friendly places in Reykjavik. In addition to the soya lattes and soya chocolate that you might find at other coffee shops, Kaffi Hljomalind has a number of vegan baked goods and entrees. There are vegan burritos (made with many different types of cooked and raw veggies), lentil pate sandwiches, date muffins, almond cakes, and banana cakes. In addition, the soup of the day is often vegan and the lasagna is sometimes made vegan (you have to ask - it's always vegetarian).
If you order the lunch special, you get a large bowl of soup, homemade bread (served with dairy-free margarine) and a glass of homemade ginger ale. It's very tasty and the prices are quite reasonable. I highly recommend ordering either the soya chocolate or the almond cake for dessert.