June is a very popular time of the year to visit Iceland. You will enjoy the midnight sun (pretty much bright daylight 24/7) and the mountain roads are most often open providing a chance to visit the highlands.
June is probably the liveliest month in the capital, Reykjavik, when locals and visitors enjoy the (not-so-warm) summer weather and swimming pools in Iceland. Excellent time to drive around the country, visit more remote areas such as the Wesfjords, Hornstrandir and the Eastfjords. Also a great time to visit the Westman Islands on the southern coast. Finally, on June 17 Icelanders flock to the streets to celebrate their independence day.