I found this property on Trip Advisor and was so glad I stayed here. I stayed in Room 90 of the Empire Apartments which is very conveniently located in Gardastraeti 40, a quiet side street within 5 or 10 minutes walk of the city centre. The apartment was very clean and tidy, and the large rooms were newly furnished and very fresh. This apartment has a large double bedroom, lounge/living room, shower-room and a small kitchen area within the hallway. The apartment is well equipped with TV and DVD, direct dial phone and free wired internet connection. Parking outside is chargable Mon-Sat, but you can park in one of the neighbouring streets free of charge instead.
Considering everything in Reykjavik is so expensive this place is an incredible bargain and should not be missed!