It is fairly easy to travel to Iceland as it is situated right between USA and Europe. The international airport is located about 45 km outside Reykjavik and when you arrive the best thing to do is to jump on the FlyBus which takes you from the airport to Reykjavik city center. For flights to Iceland check out WOW Air and Icelandair.
A good thing to do when here is to go to the Tourist Information Centre (located in Aðalstræti 2) and get a City Walks Map. From Reykjavik it is very easy to explore some of the most popular attractions in the vicinity, such as the site of the old Parliament at Thingvellir and the hot spring Geysir and the waterfall Gullfoss, the last two together usually referred as the Golden Circle. These attractions are all within simple reach either by public transport or by guided tours. When back from a day tour there is nothing better than a visit to one of many swimming pools in the city for a complete and well earned relaxation. If you have the opportunity (and the time) a visit to the Blue Lagoon, a geothermal spa and one of Iceland's most unique and popular attractions, is definitely worth visiting.