(Edited to add: Sunday September 17)
One very appreciated feature of the Hotel Berg is that their breakfast service starts at 3 am, to accommodate people with early flights. The hotel-airport shuttle service can be arranged for earlier, but starts a regular half-hour service at (I believe) 3:30. I was on the 4:30 shuttle.
The breakfast buffet is in a bare-bones cafeteria setting, with such features as communal tubs of peanut butter and jams, and a fancy coffee making machine like you see in truck stops in the US. I was pleasantly surprised by the quality of the coffee -- as good as some expresso drinks I've had made by humans.
One thing to know about early morning flights from Keflavik if you have to check luggage: about 100,000 people will be on the same errand, so you might want to arrive even earlier than the recommended 2 hours. I only had my hand luggage, so I had plenty of time to acquire second breakfast and proceed to my gate. Oh, and the other thing: this is truly a sprawling airport -- be prepared to be overwhelmed.