Another nice hotel is the Hotel Borg, it is right across the street from a public park in town, and as I remember, we walked up the street each night to a wonderful and very well recommended restaurant, very European, yet hip and relaxed.
It is an old traditional hotel updated. Most of our touring was outside the city, so we took a cab to a car rental place, drove on the right side of the road with almost no traffic and saw the geysir as it was called, and many other sights. It was a great day or two! I wish I could bring up my pictures, but they must be on that site we used many years ago for Kodak. It was early in my cruising days, and one of my very favorites, as we continued on to the Norwegian Fjords, to me the most beautiful cruising in the world.
Most of the more natural "sights" in Iceland are outside of town. Our cruise continued on to a couple more ports in Iceland which I truly enjoyed.