Great hostel! it is a little bit far from the city center, but the walk is very pleasant! The best part was being close to the thermal pools which are cheap (like 2 dollars) and full of local people, giving a glimpse in the icelandic non touristy life. Also, the rate per night of this hostel is the cheapest i have paid in the nordic countries

Stayed here during a class trip.

Nice hostel, with a convinience store (24h) in walking distance. Downtown is a short taxi trip (2000 ISK).

They served an okay breakfast, had free wifi, a nice livingroom. And clean dorms.

Their location is a little drawback, but taxi is not expensive. You can experience Reykjavik during the day, and come back to get some sleep.

Stayed for 2 nights in double room

+ Good hostel, has big living room with tv & free wifi available
+ Airport bus stops in front

- Walking to the city, is quite a walk 4 km
- Bus stop is opposite the hostel, but bus stops only once per hour

First things first. Do NOT stay at Reykjavik City Hostel under the impression that the name means you're in the middle of the city. Because it is not. It is in a very pleasant neightborhood on the outskirts of the city. You can easily get right to the city center with a brisk walk, or the bus, which is right in front of the hostel. But if your plan in coming to Reykjavik is to enjoy the nightlife, which I have heard doesn't even start to heat up until midnight, this is not the ideal location.
However -this is an amazing hostel and it is adjacent to one of the great aquatic centers of the world, Laugardalslaug. They have a huge variety of geothermally heated pools and hot tubs. It is a blissful experience immersing in the warm to steamingly hot, exquisitely clean waters.
Also, the hostel is super clean, well laid out, helpful and pretty. They have nicely equipped kitchens, and a terrific patio area in back for eating outdoors when the weather permits. They serve a breakfast in the morning, which people speak highly of, but we stuck to our homemade oatmeal for budgetary reasons. There are several pleasant rooms for lounging, vending machines, a laundry; just about anything you need. We took a private room and it was spacious with a good bed, ensuite bathroom and curtains that almost - but not completely - hid the fact that we were there on the summer solstice and it stayed bright all night long.
The downsides are few - it is quite expensive for a hostel, but then, almost everything in Iceland gave us sticker-shock, and we did opt for a private room. I was a little dismayed aout how their luggage storage was handled - we were counting on secure luggage storage as we had a late flight out and wanted to spend the day roaming the city and swimming at Laugardalslaug. They have a room in the basement for setting your luggage. The room is locked, but they just hand you the key and send you down there, so anyone can go through your stuff. Maybe Icelanders are just that honorable, but not everyone staying there is an Icelander...!
Some hostels are just more conducive to meeting your fellow travelers than others, and this one was great that way. We had lively conversations with people from all over while cooking and eating in the kitchens. Reykjavik City Hostel is full of the joy of world travel! Highly recommended!