Iceland other than Reykjavik?
I can add two restaurants to the list of Outside Reykjavik goodness:
in Vik, we ate at Halldorskaffi - http://www.halldorskaffi.is/index.php/matsedhill
GREAT fresh fish, terrific soups and breads, very good pizzas, and excellent apple pie. We ate there all three nights we were in town, partially because the alternatives were hotel restaurants, and the N1 station, but mostly because it was so good.
In Grindavik (south of the airport and the Blue Lagoon) we really enjoyed the Salthouse Restaurant - http://salthusid-english.weebly.com/
Great fish, very friendly service, best lobster (langoustine) soup I've had in Iceland (including Sea Baron and the Langoustine place in Hofn)
I got married (we eloped) by one of the waterfalls near Hotel Ranga in 2010. I arranged to have a 6-course menu for the two of us on our wedding night and 5-course menus on the evenings before and after the wedding. The food was fantastic, locally sourced and very creative, but heavy. 5 courses were more than enough and frankly, all 5 could have been smaller, especially were proteins were concerned. We opted for wine pairings each night and the pourings were more than generous. In all, we had a great time! I highly recommend arriving around noon, having a very light lunch, enjoying the surroundings in the afternoon, eating a later dinner, staying the night and partaking of the awesome buffet breakfast. You'll spend a pretty penny, but for a night it's worth the splurge.
If you get a chance to go to the Snaefellsnes Peninsula, I highly recommend a night or two at Hotel Budir. The food and experience were a little more subdued than at Hotel Ranga, but came a close second in quality. We stayed in a lovely room that had a bathtub right in the room. It was one of the best rooms in the house, but we called a few days in advance to book it and were offered the room at the regular rate, which was awesome. Needless to say, they weren't very busy that night (it was a weeknight in early October).
The food was great, with unusual options, in the Isafjordur area, but that's way off the ring road.
We enjoyed the Myvatn and Husavik areas, but our food experiences there didn't blow me away.
We spent 3 weeks driving around most of the island. If you want more details about some of the lesser known places, I'll dig up my guidebook and journal. I may have listed restaurant names in my journal, or else marked up my guidebook. I also may have detailed most of the meals we ate, particularly anything memorable. Look up my profile and drop me an email if you're interested. Always happy to chat about excellent trips. Iceland was otherworldly, in terms of untamed nature.
One place I visited twice while in Reykjavik was Einar Ben. It's not hip, happening or now, but the food was just delectable! I had the most tender and perfectly cooked lamb of the whole vacation, plus foal and a raw, cured minke whale. Other dishes tasted were a creamy smoked haddock soup, cream of celery root soup, a salt cod appetizer and a poached char entree.
We had very fine foods and unbelievable variety at Hotel Ranga and Hotel Budir. These are the types of places that bake their own breads and are fairly strict locavores when it comes to produce and proteins. Some examples are: pink footed goose, puffin and reindeer carpaccio.
In Isafjordur, I think the restaurant's name was Polurim. The food was fantastic. I think it was in a small hotel. We ate cod cheeks in a vol au vent shell with a small side salad, a sparkling mussel soup, puffin with blueberry sauce and a porpoise dish that was gamey and steak-like in look, texture and taste.
In the south of the country, we seized upon opportunities to eat the langoustines in various preparations. As a Canadian, I am a bit spoiled by our East coast lobsters. Although the langoustines are incredibly sweet, they are a heck of a lot of work to deal with when they're in their shells. They're much nicer to appreciate in a soup, IMHO.
Had we spent more time in Reykjavik, we'd surely have branched out and tried some of the more chic places. I'm sure that the restaurant scene has changed much in the 3+ years since I was there.
We really tried to eat Icelandic cuisine, rather than seek out sushi, burgers, pizza or any other influences from other parts of the world. We were forced to eat pizza a couple of times in small towns and it was pretty horrid, though fascinating to see the small-town Icelandic take on pizza.
Cured trout, char and salmon were easily had and lovely, albeit a touch salty (I'm used to sweet/salty lox). Herring served at many breakfast buffets was divine. My husband vouches for the many hams and cured meats at those buffets as well. I never made it past the herring and cured fish!
Hope this helps!