The Lighthouse is excellent for a one-night stay-over before or after a Keflavik flight. It is about 14 minutes by car to the airport. It is in a very quiet area at the end of the Gardur peninsula.
If the hotel restaurant is fully booked, as it was when we stayed, there is another within walking distance (wild and windy weather notwithstanding) - the Rostin. Unfortunately, it closes at 8 so if you're arriving later be sure to have a hotel restaurant reservation. There is nothing else for miles.