Restaurants	Address (*Multiple Locations)	Google Rating	Type of Offerings
Messinn	Lækjargata 6b, 101 Reykjavík, Iceland	4.7	Icelandic (Fish & Seafood)
Glo (​https://www.glo.is)	Laugavegur 20b, 101 Reykjavík, Iceland(*)	4.6	American/Vegan Focused
Ostabudin (http://ostabudin.is)	Skólavörðustígur 8, 101 Reykjavík, Iceland	4.7	Icelandic (Fish & Seafood)

Disclaimer: Based on my experiences and research, all of the above can accommodate gluten-free/Celiacs. However, I am not responsible for any cross-contamination that may occur, and please always remember to remind your server of your allergy/preference.