Spring and Autumn are generally considered the best times to visit Korea. Springtime in particular, between April and June can see very pleasent temperatures, flowers in bloom, pink and white cherry blossom everywhere and long periods of sunshine and clear skies.
Summers can be a bit hot and humid in much of South Korea, so travelling during this period requires some preparation for the conditions. July and August also sees the monsoon period, witnessing almost half of South Korea's annual rainfall.
The Autumn season between September and November is a perfect time to visit also, with mild temperatures, beautiful colours in the National Parks and low rainfall. Temperatures start to cool by mid October normally.
Winters in South Korea can be quite harsh, especially the further north you go. Travelling in the winter in South Korea needs preparation for very cold conditions.