Almost 20 or so years ago when I was a lot younger, my dad would run in the morning when we were at Disney World. Apparently, he was able to get through one of the gates at Epcot and ran through the park for a little while before returning to the resort. He said it was pretty cool since no one was out at all except for the people working there.
Of course now security is a lot tighter and even if you are in the park before it opens (for special breakfast or tours), if you don't go to where you're supposed to a manager or another person will lead you back to where you are supposed to be.
To the original question: my favorite running is around the Epcot Resorts. There are a few variations you can do. You can run inside the resorts (around the lake) and up to MGM. When I wanted to add some miles I would run on the sidewalk around the front of the hotels. The only thing you have to watch out for is that they don't always have sidewalks through the parking lot so it can get harry depending on how many cars are coming in and out.
I know some people who like running at Fort Wilderness as well, but I have yet to go over there to explore. As for DAKL, I don't really know of any good paths since most of the paths around the savannas are all inside the hotel.