Jim-
I think you may be talking about the Fish Company. We have made reservations there the day we get to Iceland. The Around Iceland tasting menu is supposed to be delicious. Another popular seafood restaurant, the Seafood Cellar, has closed. Here is a link:
http://www.fishcompany.is/English/About_FishCompany I was able to make a reservation on-line via email. Shouldn't have bothered with google translate-received a reply in English.
Second night we are trying an Indian restaurant with great reviews called Auster India. Here is that link:
http://austurindia.is/?lang=en We are thinking about visiting the Blue Lagoon on our way from the airport to the hotel using the flybus.