Song: Track07
Instrument: Piano
Anime/Game: Tsukihime
Artist: Unknown
Album: Tsukihime OST
Comments:
From the Tsukihime game, the song is also known as Homesickness on an official album that was released later but there are a few small changes to Homesickness that took away some of the original's goodness (for me, at least). It's a really simple, sweet melody but I haven't been able to find the sheet music for it anywhere. If you're interested, it can be found on Youtube here (http://www.youtube.com/watch?v=LIleIBSm_zc) or I can send it to you in mp3 format (or something higher, if need be). If anyone is able to transcribe it that would be awesome.

I love this song, it's just so nostalgic.

I prefer the original version too, but is that the original version posted in your Youtube link? It sounds kind of different from what I remembered, I think:
http://www.youtube.com/watch?v=kbNWTUUusfw
might be the original one.