Alfreds Apartments is also teaming up with BEARS ON ICE. Alfred's Apartments offer eight apartments in center of Reykjavik. They are fully furnished with free Wi-Fi Internet, televisions and safety-deposit-boxes among other things. The apartments are located in a quiet area of the very center of Reykjavik city.
Visit Alfreds Apartments website for more information and bookings.
For more listings, check out Gayice.is website which has a good number of accommodation listed.