When visiting Disney World, out of all the locations I've tried to watch parades, in my opinion the BEST location to watch the night parades is at the main entrance in front of the barber shop.
First, this area is usually extremely quiet, no one thinks to stand there.
Second, there is a bench there, so if you're with people who may need to rest their feet (elderly, tired, etc), and it's probably the only place to watch the parade from a bench.
Third, since crowd interaction is extremely important to the people in the parade, they tend to be a bit more "fresh" coming out of the gate. You have a FAR better chance of getting a high five, or someone twirling your daughter like a princess (Cinderella Mice, etc), or a wave from Mickey or Minnie right out of the gate.
Fourth- Since the park tends to clear out after the night parade, you're right near the exit for a quick getaway.
Bottom left, right where the red dots start, that's near the barbershop (the only one in Disneyworld), that's the best place to watch a night parade