I don't visit Seoul that often, but if I'm meeting someone there, this is one of the cafes I always go to. From the entrance you can see the cafe's logo covered in vines, and when you step into the first floor the space feels so wide and cozy that you immediately feel glad you came. It's a place where you can have a cup of coffee and chat with a friend and lose track of time.
The basement level has a large area where you can sit and enjoy a quiet cup of coffee. The rooftop lets you have a coffee while watching people pass by and breathing the outside air, but personally I recommend zoning out while looking through the floor-to-ceiling windows on the first or second floor.
If you go with a friend, it's great for fulfilling that romantic vibe at any seat; you'll get so caught up in conversation that you might not even notice the time passing until evening, so it's a wonderful place to enjoy.