Keflavik is more a gateway than a destination, but the Reykjanes Peninsula around it has genuine attractions worth stopping for. The Icelandic Museum of Rock 'n' Roll is the most surprising — a serious, well-produced museum about Iceland's outsized contribution to popular music, from the 1960s US military base era through Bjork and Sigur Rós. The Viking World Museum covers the Norse settlement of Iceland with a full-scale replica longship as its centrepiece.
Out on the peninsula tip, the Garðskagi Lighthouses at Garður are among the most atmospheric in Iceland — two towers, one from 1897, the other from 1944, standing at the edge of the land where the sea stretches unbroken to Greenland. The birdwatching around the lighthouse in spring and autumn is excellent: eiders, puffins, and a stream of migrant waders working the shoreline.
The Blue Lagoon is well covered under the Reykjanes Peninsula page. It is 20 km from Keflavik and bookable directly; most visitors pass through it on the way to or from the airport.