The best option for transportation from the Airport, if not using a rental car, is a taxi. We at START Hostel have a special deal with the local taxi service called Aðalstöð for the trip from the Keflavik International Airport to us or vice versa.
All the cars have the logo in the window of an "A" with wings, so they should be easily spotted from the other taxi's available by the Airport.
Even if taxi services in Iceland are not the cheapest, Aðalstöð offers client who ask about it right away, a fixed rate for the transport to us which could calculate to a bit under 3000 ISK or 24 Euro/27 USD. Meanwhile other Taxi services have been known to charge up to 5000 ISK (or 39 Euro/46 USD) for the same trip.
We only wish for our guests to have the best experience for their visit to Iceland so if you have any further questions about any transportation before coming, feel free to contact us at firstname.lastname@example.org with any further questions.