Sterna (http://www.sterna.is) and Reykjavík Excursions (http://www.re.is) operate regular bus service from West Iceland, South Iceland and Akureyri. If you find yourself in other parts of the country, it will be difficult to find a direct bus route to Reykjavík. The best option, if relying on buses, is to first get into the aforementioned regions and catch a bus to Reykjavík from there. This will probably require an overnight stay.
Two airports serve the Reykjavík area, one for international flights and another for domestic flights. They are 50 km away from each other.
Keflavík International Airport Icelandic: Keflavíkurflugvöllur, IATA: KEF, ICAO: BIKF (http://www.kefairport.is/...) Airport is Iceland's main international airport, and is located 50 km southwest of Reykjavík, in the town of Keflavík. Some of the international airlines flying to Keflavík include:
Icelandair - offers non-stop flights to/from New York City, Boston, Edmonton, Halifax, Toronto, Minneapolis/St. Paul, Orlando Sanford, Seattle, Amsterdam, Berlin, Brussels, Copenhagen, Frankfurt, Glasgow, Helsinki, London, Oslo, Madrid, Manchester, Milan, Munich, Paris, Stockholm, Bergen, and Gothenburg. Please note that some destinations are seasonal. Icelandair offers free layovers for up to seven nights if flying between Europe and North America with Icelandair.
WOW air - operates flights to/from: Boston, Washington D.C., Berlin-Schönefeld, Copenhagen, London-Gatwick year round, as well as summer flights to: Alicante, Amsterdam, Düsseldorf, Lyon, Milan-Malpensa, Paris-Charles de Gaulle, Salzburg, Stuttgart, Vilnius, Warsaw-Chopin, Dublin and Zurich.
SAS - offers flights to/from Oslo.
EasyJet - offers flights to/from Basel, Belfast, Bristol, Geneva, Edinburgh, London and Manchester.
German Wings and Air Berlin - operates flights from various German cities during the summer.
Delta Air Lines - operates flights to/from New York City and Minneapolis/St. Paul beginning May 2016.
Wizz Air - operates flights to/from Gdansk.
To travel between the airport and Reykjavik city center:
Flybus(http://www.flybus.is/flybus) offers regular service to either the BSI bus terminal, just south of the city center 45 minutes, 1,950 ISK one-way or 3,500 ISK round trip or directly to Reykjavik hotels with advance notice to the driver 2,500 ISK one-way or 4,500 ISK round-trip. Buses leave the airport as early as 3:30 AM. Tickets can be bought either at the airport or online.
Gray Line Airport Express(http://www.airportexpress.is/) offers regular service 45 minutes, 2,400 ISK one-way or 4,400 ISK round trip directly to Reykjavik hotels with advance notice to the driver. Tickets can be bought either at the airport or online.
Bus nr. 55(http://www.bus.is/) is the public city bus that operates between the airport and the city 45 minutes, 1,600 ISK one-way. Tickets can be bought on the bus. Check the time schedule as this bus line is mostly used by people who work at the airport and convenient for their working time. In the afternoon it goes every hour.
Taxiscost 14,000 ISK for 1-4 passengers and 19,000 ISK for 5-8 passengers.
Reykjavík Airport Icelandic: Reykjavíkurflugvöllur, IATA: RKV, ICAO: BIRK
Air Iceland - operates domestic flights to Akureyri, Egilstaðir and Ísafjörður, international flights to the Faroe Islands and several airports in Greenland. Leaves from a terminal on the west side of the airport.
Eagle Air - operates domestic flights to Bíldudalur, Gjögur, Sauðárkrókur, Höfn and Vestmannaeyjar. Leaves from a terminal on the east side of the airport.
Several cruise liners stop in Reykjavík each summer, mostly arriving in Sundahöfn which is 3 kilometers east from the city centre. Cruise Iceland is a website run by several companies that service cruise liners in the country and has a list of companies that sail to Iceland: (http://www.cruiseiceland....).
Reykjavík itself is not served by any ferries, but if you have an abundance of time it is possible to take the Smyril Line a cruise company based out of the Faroe Islands from Hirtshals or Esbjerg to Seyðisfjörður a small town on the east of Iceland, via Tórshavn. This service is on the expensive side, and puts you on the other side of the country. However, it offers the possibility of bringing a car, which can be one of the best ways to travel around Iceland. If you take the ferry and drive from Seyðisfjörður to Reykjavík, you should plan to spend the night somewhere along the way.
Of course, if you have a boat capable of crossing the Atlantic it is possible to sail to Reykjavík. Check with the port authority, the United Ports of Faxaflói (http://faxafloahafnir.is/...), to find out about harbour options.
Three main roads serve as entry points into Reykjavík:
Reykjanesbraut Road 40, enters the city from the west linking it to Southwest Iceland and Keflavík International Airport;
The Ring Road Road 1, enters the city from both east and north.
If you're driving into town from South Iceland or West Iceland, beware of some quite heavy traffic jams on Sundays when people are going back home after a weekend away. This mainly applies during the summer, and becomes even worse on Mondays after three-day weekends, not to mention if the weather has been good.
There are rental car services all over Iceland, and many in Reykjavík. The cheapest car at the cheapest dealer you may find would average out to about 5500 ISK each day. If you intend to just stay in Reykjavík, renting a car is not necessary as the bus system is great and it is easy to walk around. If you plan to leave Reykjavík and go to the countryside, then renting a car is the best way to experience Iceland.