One of the place you won't miss, if you are walking up and down Reykjavík main streets in city centre.
Café SÓLON is a brasserie type of place and also a art gallery. That's a good spot to grab a soup or a sandwich before you head to some afternoon excursion for example.
Their club sandwiches are massive and very tasty. You'll find Turkey, chicken and bacon in there, served with french fries, enough to feed a man for the day. Thee bagels are also a very good option there.
By the time we went there in the early spring, it looked a bit like a toursits place, but locals talk also about this place so when the summer days are coming it might be a pleasant place to have a fast and affordable simple meal. And more thing to add here, the staff is actually quite friendly and helpful!