During a parade is one of the best times to go on rides, because so much of the crowd is pulled away to see the parade! As long as you are in a "land" before parade time, you should be fine. There are crosswalks staffed by Cast Members for foot traffic, until just before the parade passes by. I'd say either Fantasyland or Tomorrowland are great places to be during the parade. Adventureland too, really - the parade passes through Frontierland, so I'd avoid Splash and Big Thunder Mountains during that time.