In 2010 a memorial has been made round of the tree which The Girl and Kyun-woo buries a time capsule under it. The memorial is called Time Capsule Park, and it's made because of the 10th anniversary of the film. The exact coordinates of Time Capsule Park are (37° 12' 05.60" N, 128° 41' 19.50" E).
The trivia item below may give away important plot points.
After the Girl talks to the old man for the last time, as she looks off into the sky, a small UFO hovers across and zips off real quickly. It's been said that the UFO is actually a time machine that KyunWoo, as an old man, used to revisit his past. The old man also makes a brief appearance near the beginning of the film when KyunWoo and the Girl meet for the first time.