This place was great and fairly cheap:

http://www.kvasir.is/butterfly/

we went in december and stayed at the floki inn—it’s more of a ‘guest house’ than hotel, but i travelled with a friend and we had two twin beds, a kettle, television and refridgerator. we also had a 5 minute walk to the centre and free breakfast included. food is very expensive in iceland so that was a nice advantage. The Floki’s owners have three other guest houses and hotels around the city, and most of the hotels are very close to the centre.

try the website
http://www.innsoficeland.is/iceland_accommodation.html.

We stayed at the “Ugly Duckling” which is the translated name, but everyone knows it as that. EXCELLENT location and great seafood buffet each night. http://www.andarunginn.is/display.php

Keep’s name is Asa (pronounced Oussa). Walking distance to everything…from the nightlife, to the interesting shopping Reykjavik has to offer. It was the cheapest we could find, but you will come to grips that everything is Extremely expensive.

Kevin-

butterfly
http://www.kvasir.is/butterfly/

great people – 20 steps from downtown but on a very quiet street. Super clean.

It’s not a hotel, but the Salvation Army hostel is a great and cheap place to stay. They don’t allow alcohol, though, but I think it’s the cheapest place around (or at least was a few years ago). Close to everything, as are most places in Reykjavík.