The nearest "good" restaurant to Hotel Cabin is reykjavikhotels.is/grand_hotel/… which is within easy walking distance. I've never eaten there, so no comment.
The next nearest, walkable, but more than double the previous distance, is http://www.vox.is/ which is at the Hilton Nordica Hotel. Personally, I don't find the ambience at Vox to be at all attractive, but many people do like it.
Probably Perlan http://www.perlan.is/index.php?lang=en is then the next nearest, slightly further away but in a different direction to Argentína Steakhouse www.argentina.is/template21086.asp… I guess that I've got bored with Perlan over the years, but my guests invariably love the place. The menu is always good, and it's not so expensive as many imagine. The view is simply the best in Reykjavík. I began eating at Argentína nearly 20 years ago, when it first opened, but after a few years I became somewhat tired of steaks, and of the prices which were very high. I've hardly been back since, although friends do speak very highly of the place. You really do need a taxi to either - my current guesstimate would be kr. 1200-1500 each way.
You might find this useful http://www.gastroshark.com/home/
Within these distances are a number of other more modest but still good restaurants. If you want to find out more then look at visitreykjavik.is/desktopdefault.aspx/…
The dress code at any of these restaurants is smart casual. But, you will find some visitors, particularly in summer, in jeans and t-shirts. Especially at weekends you will find a good percentage of Icelanders in jackets & ties, or equivalent for ladies, which is what I believe the previous post means by "evening clothes" - most definitely NOT dinner jacket ("tuxedo" for our North American friends, "smoking" for Icelanders).