Recently i´ve had problems opening youtube on my Safari. Just wouldn´t open the site.
I´m using a Macbook (the white one). I fixed it by doing the following:

1) Open Safari 
2) Go to Preferences
3) Choose "Security"
4) Choose "Open Cookies"
5) Delete all youtube entries in Cookies
6) Re-open youtube.com

This worked for me. I hope it works for you!