Prison & Sewers - 4:53 (improved version after feedback from smashly below):
http://youtu.be/jNOmFh1rIsA
Feel free to check out the rest of the playlist (w/ commentary):
@ http://www.youtube.com/playlist?list=PL0A042B3D1E37BDDD&feature=view_all
Note: The reason I don't add the Dunwall Tower intro, Blink tutorial or Weepers tutorial to the videos is because they're too short and linear to really add anything extra to the speedrun. You're gonna do those missions pretty much the same way, whether you speedrun or not. Also, the second mission is necessarily the longest in the game, because the 2 extra runes from Granny Rags allow you to upgrade Agility and Blink 2 much earlier, saving you a little time.