We drove to Keflavik from our base in Reykjavik, it is only about 45 minutes easy drive and is the location of the main airport (but also a US military installation).
The area around Keflavik is very interesting and has some attractions that are well worth seeing. We didn't really see any tourists around, so most people seem to miss this area off their itinerary. This is a real shame, we really enjoyed it here.
For 55 years a NATO base here protected the island from potential Russian invasion. At the end of the Cold War, the American led contingent left, but right up until 2006, this was an important place for the locals to work. We drove past the old base and all its buildings. It is huge - at one time 6,000 people lived at the base. You can still visit, everything is in really good condition. Many businesses have now opened up on the base - there is a big problem for them though. The power supply is based on the American system!
We explored a little around the harbour - it is very calm, still and scenic. You can climb over the rocks, take in the calm views over the water and explore an old boat.
Look for the Black Cave of the Giantess - follow the enormous footprints to find it. This is the "home" of a giantess, she is a character from an Icelandic children's book - Sigga and the Giantess. The cave was opened in 2008. Sigga and the Giantess was the first of 16 children's books written from 1959 onwards.
It is very quaint. You can go into the cave - we found the giantess sitting in a chair, breathing, snoring and making all kinds of rude noises. Our son loved this! She is supposedly 400 years old, has eyes the size of footballs and sits in an enormous rocking chair. There is also a giant bed in the cave, children can climb onto this too.
There is an interesting little museum close by - the Duushus. It is free, and well worth spending a short while exploring inside. During our visit, they were repainting and fixing up most of the rooms and it was not due to fully open until June. We were able to explore 2 of the exhibition halls though. They had a display of model ships which were all made by a local man. We enjoyed especially the exhibition about life in Iceland many years ago. They had a mock up of an old corrugated iron Icelandic house and all the information was in English.
The coffee shop in the museum is also quite nice for a snack and a drink.
The museum staff were extremely helpful and gave us a driving route around the peninsula with lots of suggestions for interesting places to stop and see. These were places we hadn't found in any literature, or in any of our planning, so we were very happy with that.