The parade begins at the Pier near the Orange Stinger and runs toward the entrance. They changed it so that it only runs this way in an attempt to prevent the crowds from trying to get back to DL to watch the fireworks.
I actually prefer to watch the parade from down in the pier area or near Golden Dreams theater. It seems much less crowded than in Sunshine Plaza. I usually can beat the parade to Sunshine Plaza by walking through the back GRR trail area, Condor Flats and then slip out of the park while the large crowds are still watching the EP in the plaza area.