The city centre, not being a large area, can be easily explored on foot. To rent a car or a taxi is an option, but an expensive one. To rent a bike can be fun in the summer, although Reykjavik is not as bike friendly as it should be. Perhaps it is best to use the municipal buses. It certainly is the cheapest way of getting around. The Reykjavik Card is a cheap, easy and convenient way to enjoy all the best that Reykjavík has to offer. It gives a free access to many museums and galleries and also to the Municipal Bus Company, the Thermal Swimming Pool, the Family Park and Zoo and discounts on many services and products. In the summer of 2001 such a card valid for 72 hrs. cost 2000 Ikr or about 20 USD. Also available 24 or 48 hour cards.
There is an airport bus going between kflavik and the BSI bus station in Reykjavik. From the bus station near the domestic airport terminal it's a 20 minutes walk to the central streets of Reyjavik. There's a taxi stand at the BSI, as well as other local buses.
Cost 1100 per person Keflavik-Reykjavik, all destinations. Ticket machine (cc or cash) as you exit the airport and the BSI. Bus departures coincide with arriving and departing flights. Check schedule as soon as you arrive just to be sure. Leave the BSI 2 hrs prior to your airlines' eparture - at least.
I'm not much of a fan of organized group touring, but I think it does make sense to take the Reykjavik Excursions coach out to the Blue Lagoon, particularly if you are planning to make the spa your final Icelandic experience before heading out to Keflavik airport. That's what I did, and I can't think of a better way to arrange a leavetaking of this fascinating volcanic place. I took the "Relaxing Blue Lagoon" excursion, leaving the city at 11.00, and leaving about two hours of soothing spa time before getting back on the coach for the airport.
We invested in a Tourist travel card for the buses, so you can hop on and hop off for the day at a cost of aprox. £12 pp, included in this price are the childrens zoo and many of the museums and art galleries.
Keflavik Airport handles all international traffic and is likely your point of entry into Iceland.
The airport is also roughly a 45 minute drive to Reykjavik. The best and cheapest way of getting from the airport to the city center is to use the FlyBus, which costs 1150 Kronur (about 25USD).
The bus will drop you off at the BSI station, which is Reykjavik's main bus station. From there you can either take a short cab ride or a city bus ride into the center.
As there are no trains in Iceland and car hire can be quite expensive, buses will have to suffice for the more budget-conscious traveller. Roads won't be very busy anyway: it's a big country for so few people!
There is a Flybus that operates from Keflavík airport to Reykjavík city centre. The journey takes about 50 minutes, is around 45 kms long and costs ISK1100 one-way.
Thanks to our friends at Lonely Planet, I was able to upload a small map of Iceland to illustrate the country and its distances.
If you dont own a car (i looks like if everyone has got thousand of them), the best way you can move around Reykjavík is by bus ( actually there must be the only way since there doenst exists either trams, metros or trains), buses run from early in the morning until 11pm, they are yellow/orange and you pay 220 ISK for a single ticket, the drivier never gives change back, so u better pay with the exact import.
Flybus - From Keflavik International Airport directly to your hotel/hostel. U.S. planes arrive around the same time in the morning so the buses will be there waiting. Takes about 45 minutes from Keflavik to Reykavik. Cost approx $10 US.
Walking - A good way to see the city if your lodging is in or close to the city center. Most of the city attractions are within walking distance of each other.
Museum Bus - A service provided to vistors which runs between the museums and attractions.
Reykjavik Excursions - Has guided city tours or combination tours with horseback riding, blue lagoon, etc.
Altough Icelander seems to have car (everybody) there's quite good public tranportation In Reykjavik. Just go to the bus station and take a map or ask more information. My Icelandic friens told me that busses are bad and slow, but I was very satisfied. I saw much more than city centre by bus. Kopavogur is worth of visiting, and Hafnafjodur too.
But if you want just see Reykjavik I prefer walking. The city center is quite simple and you'll se much more by walking. I use to walk to my work and always from home to shop and to gym. Busses I use to when I wanted to see places outside Reykjavik. My flat was located in the place where is red cross. It was good place to live, everything was nearby. Public transportation is not very cheap, so if you're going to work or study to Reykjavik, try to get flat from center. University is also there.