Icelandair departures, with destination Zurich, in 2018 were at 7 in the morning. Nothing much to do, except breakfast. There are many hotels in Keflavik or near the airport.
One good option is hotel Aurora Star. It is just a few minutesby foot from the airport, it serves early breakfast and it allows you to retourn your rental car the evening before (which saves a bit of money).
Let’s put advertisement aside. Here you will find a gallery of pictures taken by my father in the last week. Enjoy!