A great value guest house, around a half hour's brisk walk along the beautiful sea front to the city centre.
My friend and I could simply not afford to stay in a hotel, and then I saw another good review of Guesthouse Bina here. We booked, and were absolutely delighted with our stay. The rooms were pleasant and cosy, Bina herself was totally charming, and her breakfasts (a very reasonable 1,000 krona) were delicious and generous. Her flat was beautifully clean, and sharing a bathroom was never a problem.
Anyone worrying about the distance to town, yes, it is a bit of a walk. But it is an utterly beautiful walk along by the sea. Every day we saw sea birds diving for fish and the waves and the snow capped mountains, and said to each other how lucky we were to have to do the walk - staying in the town centre we'd have missed it all. After all, if you want to just see city streets, why are you going to Iceland?!