Hi there, I would not say that you need to take cash with you, you can basically pay everywhere and everything in Iceland by credit card, even an apple.
If you want to have some cash you might better get something by using the ATM instead of changing money in your home country or at the airport, unless your bank charges crazy high fees. In regards to changing money you get better rates in Reykjavík than in the airport. Only banks can change money and they are usually only open until 16:00.
USD or Euros are generally not accepted but you might be lucky in some touristy shops, but I would not count on it :-/