I think it totally depends on what you and the kids want to ride. If you want to ride things like Buzz and Space, then I'd stand just at the end of Main Street, where the path circles around in front of the Plaza Pavilion and you can rush from there to Tomorrowland while the parade is finishing up going around the Hub.
If you want to ride things in Fantasyland, I'd personally stand either right in front of the castle (if you can pass through it) or just over the bridge into Liberty Square, where the path takes off along the moat and up to Fantasyland.
If you want to see the Country Bears, or ride something like the Tiki Room, I'd stand right in front of Country Bears.
If you want to ride something in Adventureland, *or* want to attempt to catch the parade twice, I'd stand pretty much in front of Casey's Corner on Main Street, where you can take off past the Crystal Palace and into Adventureland. If you're trying to catch the parade twice, then go all the way through Adventureland past Pirates and you might be able to catch it at the end of the route.
If you want to ride Haunted Mansion, stand where the parade makes the turn in Liberty Square.
If BTMRR or Splash, stand at the edge of the path leading to Splash, where the parade goes back to the back, making sure to be on the Splash and Thunder side of the route.
It really totally depends on what you want to do.
