Due to problems, I've decided to completely re-install Skyrim. I've heard it recommended that Skyrim (and all other Bethseda games, for that matter) should be installed outside of the ProgramFiles folder. Is this true and if so, is just on the c drive fine?

Program Files on the system's root drive is protected and shouldn't be used.

For reinstallation/uninstallation help in general, here's a link to a previous topic that just about covers it: http://www.gamesas.com/topic/1381322-want-to-do-a-proper-uninstallreinstall/