Besides the obvious stated above, I would advise:

Sjávarkjallarinn (The Seafood Cellar): www.sjavarkjallarinn.is
Vox: www.vox.is
Argentina: www.argentina.is‎
Humarhúsið: www.humarhusid.is‎

If you have time, drive two-three hours to Hótel Búðir: www.hotelbudir.is‎