We recommend using DoHop when searching for car rentals in Iceland. The rental car companies are very similar but this search engine will help you find the best deals.
If you are not planning on renting a car, the most common and best way for small groups is the FlyBus from Keflavik International Airport.
When it comes to selecting the Flybus you have two options: the regular Flybus which takes you to the central bus station at BSÍ and the Flybus+ which drops you off at a selected location.
Your nearest drop off is bus stop 12 – Höfðatorg
The public bus nr. 55 travels regularly throughout the day from the airport to the capital area. Please note that the bus does not always drive all the way to BSI bus station, downtown Reykjavik. In those cases the last stop is at Fjörður, in Hafnarfjörður, which is a town just outside Reykjavik.
You can see the prices for bus nr. 55 here
You can purchase your bus ticket at the airport with card or cash.
Please note that while this is the fastest way of commuting from the airport, Taxi is also the most expensive one.
The price for 1-4 people is 16.500 ISK and 21.500 ISK for 5-8 persons (this price can vary – price collected November 2022).
You can book a taxi in advance by sending an email to firstname.lastname@example.org
Tel.: +354 5610000
See more info here