Keflavik Airport is located an hour away from Reykjavik. It’s actually a small airport so don’t worry about getting lost or not finding your way around.
To get to the city center, you have four options.
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Rent a Car
If you can drive and have a driving license, you might want to consider this. I mean, REALLY consider this. Renting a car is by far the cheapest (if you’re a party of 2 or more) and most convenient way to get around Iceland. If you’re planning on renting a car to tour anyway, you might as well pick it up at the airport. You can arrange this before your flight or rent at the airport.
If you can’t drive for whatever reason, you can:
Take the Public Bus
This is the cheaper bus option. Iceland has a Public Bus System called Strætó, and it runs Bus 55 that plies the Keflavik Airport to Reykjavik route. Just look for the BUS 55 sign outside the terminal. Its final stop is the BSI Umferðarmiðstöðin, which is the city’s main bus terminal. You can take another bus or you can walk to your hotel from here. The downside here is that it’s not as frequent as the private buses. You may check the timetable here. Fare: 1680 ISK (13 Euro, 15 USD).
Take a FlyBus or Grayline Bus
Most tourists end up taking this because they have very visible booths by the terminal exit. It’s slightly pricier than the public bus and they charge more if they drop you off at your hotel. Note that if you choose that they take you to your hotel and if your hotel is located in the Old Town, you will be switching to a smaller mini-bus/shuttle at the terminal because big buses are not allowed in the area. Here are the rates:
To Reykjavik BSI Terminal: EUR 20 (ISK 2500)
To your Hotel: EUR 24 (ISK 3000)
To Grayline Terminal: EUR 15
To your Hotel: EUR 17
Take a mini-bus or shuttle
There are also other companies like Reykjavik Sightseeing who could take you straight to your hotel without stopping or switching vehicles because they use a smaller shuttle all the way through. Fare: ISK 2990 (EUR 24).