The proprietors sometimes get a little undeserved heat from reviewers, for their particular ways. For example, check-in is 4 pm. Not 3:30. If you're early, you leave your bags up front and go off to explore the neighborhood. Also, you're asked to leave your key at the desk in the morning and retrieve it whenever you return. And, there is a fee for Wifi use, so be warned. Parking can fill up quickly in front of the hotel, though there's spacious, free public parking around the corner.
We had no issue with any of this. These gentlemen do most of the work here themselves. They run a tight ship and require adherence to these easy restrictions. Once you accept that, you're in for a great and welcoming experience.
The Phoenix is perfectly situated on Laugavegur Street. It's a nice walk down the length of the street, through town. The gentlemen who run the establishment are fussy, precise, and extremely helpful. You absolutely cannot do better than to ask these two about your itinerary through the city and country. The building is oldish but nicely restored and kept up. Our room was top floor, overlooking the garden. In late winter this view is a little grim, but looks like it would be lovely in summer. It's a bit of a climb with heavy suitcases up the winding stairs, be warned. Got a great supper recommendation - Pots and Pans, three blocks away. Breakfast is a little minimalist, but satisfying and served with as much conversation as you like. For us, the Phoenix is a definite repeat next time in Iceland.