Summer is definitely the best time to go, and even then the...
... tourist traffic is still mild. The midnight sun is a beautiful sight and one definitely not to be missed. It is easy to lose track of time when the sun is still high in the sky at 11PM. Early or late winter, however, can be surprisingly good times to visit. In late January, daylight is from about 10AM to 5PM, prices are lower than in the high season, and the snow-blanketed landscape is eerily beautiful. (Some sites are, however, inaccessible in the winter).
This land of fire and ice is not only unique and a wonderful natural phenomena that intrigue visitors, the Icelandic people, descendants of ancient Norsemen and Celts, are intriguing too, and are welcome additon to visit to this country. Most of the country's popular tourist attractions are in the S of the island near the capital, Reykjavik.