Looking for a good one day trip just outside of Seoul? Why not head to Nami Island?
Nami Island is about an hour out of Seoul and is easily accessible by train (ITX) or bus. If you're a fan of Korean dramas, you might recognize that the drama Winter Sonata was filmed here!
The tall, matasequoia trees are a perfect place to take a couple photo and it's a relaxing place to hang out even with just friends and families. The large open space also makes it a good place for a picnic or rent a couple/family bike to tour the island!
You can actually zip-line to the island and take the ferry back or take the ferry both ways (make sure to show your passport and you get a 2,000 won discount!). Be aware though, that the wait time for the zip-line can be extremely long!
You also cannot leave Nami Island/Gapyeong area without eating Dalkgalbbi
The Chuncheon area is famous for Dalkgabbi. I didn't know Korean grilled chicken wrapped in lettuce could be so good. And yes, it actually does taste a little different (in a good way) from the restaurants in Seoul. There are a million Dalkgalbbi places near the Nami Island Pier but I would recommend Nami Anbanji BBQ Chicken.
If you enough time, try the rail bikes at the Gapyeong Rail Bikes. It is a quick 10 minute bus ride from Gapyeong train station and the rail bikes will take you through a scenic route - perfect for both couples and families. Make sure to reserve them online beforehand!