MK -
Tom Sawyers Island - Perfect spot to let the kids run and burn off some steam.
The rose garden next to the castle.
Fantasyland - Fountain area by Gaston's Tavern
Tommorowland - not a spot but a ride. The People Mover - very relaxing ride.
Adventureland - benches opposite of Pirates (not really quiet but enough spots to sit and relax)
Main Street- the little streets off Main Street next to the shops.
A train ride is good help at soothing a melt down or help relax tired kiddos.
EPCOT -
All the benches around the lagoon at World Showcase.
Future World - The area between WS and FW.
AK - Love the area by Flame Tree BBQ. Find a spot to sit by the water or across from the entrance of Flame Tree (sit a watch the bands play etc.. ).
Dinoland is great spot for the kids to explore and burn off some energy.
HS - Benches by Echo Lake is pretty place to sit and relax.
Also, I second the Streets of America as it always seems to be always quiet.
Fountain by Muppets 3D is good place to relax
When my kids were younger, the melt downs would start around 11:30 - so we would usually head back to the hotel to swim, eat and nap. Not sure if it is possible for you but it sure did help in our case!
