Here is The Traveling Professor's top-secret list of the best places to eat in Reykjavik, Iceland.  This list was compiled by The Professor over years of research.  It includes restaurants that are the most desired, most delicious, and most secret in all of Iceland.  Feel free to visit any of these restaurants or dining spots in Iceland, but don't share them with anyone, because it will then become impossible to get a meal there!

Snapps (Schnapps):  French bistro in a casual atmosphere.  The croque monsieur is The Professor's fave.
Porsgata 1
101 Reykjavik 

Rossopomodoro (Italian):  Good, solid Italian food with friendly service.  Inexpensive by Iceland standards. 
Laugavegi 40a - 101 Reykjavík 

Café Solon: Under new ownership and centrally located, expect a good burger here. 
Bankastræti 7a
101 Reykjavik 

Duck & Rose:  In the middle of the city, the Duck features, well, duck. Also serving Italian, beef, fish, and something for everyone. 
Austurstraeti 14
101 Reykjavik 

Reykjavik Fish Restaurant:  The best in Fish & Chips and not too expensive.
Tryggvagata 11
101 Reykjavik 

Sjavargrillo (The Seafood Grill):  A bit on the eclectic side, expect some creative fish dishes, including lobster, here. 
Skolavoroustigur 14
101 Reykjavik 

Apotek :  Elegant and extensive, this is the perfect place for a celebration.
Austurstraeti 16
101 Reykjavik 

Grillmarkaðurinn (The Grillmarket):  Small dishes, big dishes.  This is the place for puffin or whale.
Laekjargata 2A
101 Reykjavik 

Baejarins Beztu Pylsur:  By far, the most well-known dining spot in Iceland.  It's a celebrity hot-dog stand.  The best hot dogs in Iceland. 
Tryggyatagata 1
101 Reykjavik, Mioborg

Join The Traveling Professor on a small group tour to Iceland.   See:  https://travelingprofessor.com/Tours/Iceland-and-the-Northern-Lights