It is VERY important that you do not install Skyrim to Program Files or Program Files (x86) directories, if that is where steam is installed. Not a simple logout, that Cleanup! will want you to do. CCleaner is also good for this, or if you have it Cleanup! 4.5.2 is also VERY good at this (plus it makes a dandy flushing sound, reminding you that you're getting rid of all of the shit!). The next step in Phase One is to run a temporary file cleaner. I HIGHLY suggest using this guide for a totally new save). Open %\users\\My Documents\My Games\Skyrim and delete everything in this folder except the 'Saves' folder (if you'd like to keep previous saves. CCleaner and/or Revo will make sure that these registry items have been properly removed.
The reason for this, is because there will be registry items left over if you just delete the content. I personally suggest using a tool like CCleaner or Revo Uninstaller to do this, instead of simply going into Steam and clicking 'Delete Local Content'. Lets start by totally uninstalling your current installation of Skyrim. A clean install of Skyrim, and some random OS tweaks to help performance