No, you don't need any cash in Iceland. And yes, you can pay everywhere by debit or credit card. Note that some places (such as unmanned petrol stations) only accept credit cards with a 4-digit pin.
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There is no obligation for Icelandic businesses to accept any currency other than Icelandic króna. Places regularly frequented by tourists such as restaurants, bars, hotels, and tours are the most likely to accept foreign currencies, although you should never rely on them taking anything other than ISK.
Entry, Exit and Visa RequirementsYour passport should be valid for at least three months beyond the period of stay if you plan on transiting a Schengen country review our U.S. Travelers in Europe page. You will need sufficient proof of funds and a return plane ticket.