Hey Arunima , Its March to May, also the spring season in Jeju island where you can enjoy stunning cherry blossoms and Canola flower.... And September to November when it is Autumn there with a mild rainfall at this point of time ... Happy Travelling!!!
The best times to visit Seoul are from March to May and from September to November, when the weather is mild (average daily high temperatures stay below the mid-70s) and travel expenses are low. Source : UC
Dear Arunima, South Korea has four distinct seasons. Summer from June to August are hot and humid, winter from December to February are icy cold and dry, autumn September November and Spring, March - May are the ideal times to visit offering warm sunny days with clear blue skies ripe for sightseeing.