Iceland has both super markets and 24h stores. The prices vary because of the opening hours f.e. the 24h stores are much more expensive but necessary sometimes.
The cheapest store for many years in a row is Bonus (www.bonus.is). The next in line and known for good quality is Kronan (www.kronan.is). Both of these stores have a health sections for special needs and of course a variety of food.
We recommend renting a Motor Home or Camper in order to profit from the lower food prices. You can of course still go to a Restaurant occasionally to skip cooking. After all you are on holiday. During the pick up procedure a member of our staff will point out the local stores on a map. If possible pick up the vehicle during opening hours of the grocery stores and remember that the instruction can take 1 hour.