Where can travellers find delicious and cheap eats during their stay in Iceland’s capital,Reykjavik? How can one eat delicious food without breaking the bank? Discover the top 10 cheap restaurants in Reykjavík. Being an island with an extremely small population which relies heavily on imported goods and raw materials, Iceland is a relatively expensive place to visit. Thankfully, eating cheaply in Reykjavík is more than possible, though it does take some navigating and prior knowledge of where the best deals are to be found.