I don't think there's anything wrong with going straight to your computer when you wake up. It stops me going back to sleep, and I need to check my Internet Empire is still functioning happily.
The thing where I find I waste time, is that, when I'm between useful tasks on the computer, I do exactly what you describe. I get to a natural break in one useful task, and if I'm not immediately inspired to do something else useful, I default to sitting there checking news sites, forums, torrent sites.
I'm trying to reprogram myself to get up at this stage. Perhaps I'll add some Bookmarks/Favourites or Toolbar Links... "Go and Juice Some Fruit" or "Get Some Fresh Air" or "Tidy My Desk"