Suggest booking an Airbnb and grocery shopping. We made Selfoss a home base for sightseeing, and bought groceries / booze from the local supermarket and Vínbúðin (government-run liquor stores) so we could mostly “eat in” and pack picnic lunches and snacks to bring on our sightseeing jaunts (we rented a car). That way we could save money to eat out when it was really special.

You can also find fast-food chains like Subway and KFC in Reykjavik ; we had good luck with some very tasty prepared sandwiches and pizza at some 24-hour convenience stores in Reykjavik.

I didn’t this myself, but next to baggage claim at the airport in Keflavik is a duty free shop. Those often have sales, plus tax free. Not food-food but could get sweets, beer, liquor, snack foods, etc.