One thing you should keep in mind any time you see an alligator out of the water is that they are very quick on land -- especially the medium-sized ones, 4-8 feet. In all probability, the only time you would see that speed is when they were fleeing, but there is no sense being stupid around a large carnivore like an alligator.
At Everglades National Park, we recommend that people stay 15 feet (5 meters) away from alligators. However, those are alligators who we protect from feeding and harassment. At a place like WDW, where they have surely had plenty of both, I'd stay somewhat further away than that.
I probably wouldn't go within 25-30 feet of an alligator at WDW, and I'm very familiar with them and know what to watch out for in their behavior.