There are several local and international car rental companies operating at Iceland’s Keflavik Airport, including Hertz, Avis, Budget and Europcar. There are also plenty of options for private tours of Iceland.
All driving licenses issued in the US, the EU / EEA, and Canada are valid in Iceland. For other countries, check that your licence has a license number, a recent photograph, has been printed in Latin characters, and is valid for the dates you’ll be driving. Otherwise, you’ll need to obtain an International Driving License before you leave home in order to drive in Iceland.