Exeter Hotel is a really nice design hotel in downtown Reykjavik, near the Old Harbor.
The room I stayed in was super nice. Beautiful bathroom and comfortable bed. The perfect place to recover from a jetlag or enjoy a few nights in Reykjavík. Downstairs at the entrance there is also a cafe where they played life music the night I was there. But you could also go for the relaxing experience by enjoying the sauna of the hotel.