So I general I have to say that you get a better value eating out during lunch time rather than in the evenings. Obviously that only takes into account the food itself but not the atmosphere which understandably is different during different times.
There are quite a few options in the above 20$ (19€) range but I would like to focus on the below 20$ this time and where you can get the best value for that amount.
I would like to point out that it does not make sense to eat fast-food or at cafés during lunch time. A bagel and a cup of coffee is uncomfortably close to 15$ and a Burrito at Serranos or a Subway sandwich will cost somewhere around or above 10$. I hate to admit it ... but if you want to get something cheap you best value in that area is probably Dunkin Donuts I have not been there myself and cannot guarantee the quality but anyways...
My view of the fast-food option of course excludes the Bæjarins Bestu Hot Dog stand but you were going to try that anyway and it is kind of a must when in Iceland.
For the best value lunch I would like to point out a few places in no particular order.
Snaps Bistro is a fantastic place both during lunch and dinner time. The atmosphere is awesome and their fish of the day for 1,990 ISK (18$) makes it one of the best value restaurants during lunch time. But be careful if you are going to have anything else than the fish of the day the price will spike considerably or give you worse value.
Messinn is a relatively new restaurant and I am not sure if that is the reason that they price them below similar quality restaurants or not but this gives you a very good value for lunch (and actually evenings as well). They serve a traditional Icelandic course, Stewed fish, in a more modern way for 17.5$ and it is one of the best I have had. Other courses are also in a good price and are kept under the 20$ limit. In addition the portions are large (in Icelandic standard)
During summer Resto also reaches the list of good value lunches but sadly they are not opened for lunch during winter time. They have a very simple menu during lunch time but always good. I can also recommend this restaurant during evenings and gives you a good value for your money.
Lastly, but by no mean the least, I have to mention Gló which is the best vegetarian option in Reykjavik. With 4 different location in the capital area you can not be far from it. Even for the none vegetarians this is good food and super healthy and I certainly can recommend it.
I will add to this list if I try (or if someone pops into my mind) more restaurants that gives you excellent value for under 20$