There are two grocery stores/supermarkets in the city center, one is called Ten Eleven (open as you might presume, 10AM-11PM, daily) and the other is Bonus. Bonus is on Laugavegur, and Ten Eleven is only 3 minutes walk from Salvation Army Guesthouse, headed towards Laugevegur. I believe Bonus is slightly cheaper, but Ten Eleven has longer hours.
As is expected, it is significantly cheaper to buy food at the store to prepare in the hostel's kitchen. However, if you're craving a protein fix, or just want a great, cheap meal in general, authentic Mexican food is available on Laugevegur, on your way towards the Landsbanki...very reasonably priced and very delicious! They use some kind of tangy bbq sauce. Two crispy chicken tacos is only 395kr. You can supersize as well.
Restaurants are expensive enough that you might consider fasting as not only a cost-effective but potentially enlightening alternative to eating. Sooner or later you're going to need some fuel though, so check out Cafe Paris (Austurstraeti 14), a good choice with its central location and affordable, light meals. For sandwiches, soups, and pastas, check out Cafe List (Klappasrstigur 26) and Cafe Hus Malarns (Bankastraeti 7). Another rather inexpensive option is the bagel cafe about two thirds of the way down Laugavegur. Here at the cozy, friendly Reykjavik Bagel, they serve a sumptuous array of bagel sandwiches, most for under US$8. My tomato, mozzarella, and basil on toasted bagel cost US$5.
For another totally cheap delicious eat, make sure to hit the hot dog stand by the harbor! On weekend nights at 5 and 6AM, when people actually decide to start leaving bars and clubs, you'll find everyone out in the midnight sun, chomping on an unbeatable hot dog!
In fact, petrol stations are a surefire hot dog destination, and some of the cheapest places to grab a bite to eat. Most have a grill where you can also buy decent and filling sandwiches, fries, and of course general gas station-type snack foods.
Traditional Icelandic food is definitely a story to tell the grandkids. The splurge could be worth it - it's not everyday that one finds rotten shark meat, pickled ram's testicles, and singed sheep's head among the few offered entrees at a local restaurant. If extreme eating is a hobby of yours, a buffet might be a good way to tackle several legendary dishes in one sitting. There is a traditional Icelandic buffet restaurant located on the same block as the aforementioned cheap Mexican restaurant. I believe the dinner costs about US$25-30.
Just because Iceland is expensive, you certainly won't have to starve. I became a familiar face at the grocery store and spent about US$10 a day eating peanut butter and banana sandwiches for breakfast, tomato and cheese sandwiches for lunch, an apple/muffin/cookies for snack, and spaghetti with tomato sauce and broccoli for dinner. If your budget is even tighter than mine was, a) you probably should save Iceland for a later date or b) get full on free samples of fish cake and yogurt sauce at the supermarket!
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