This is all from memory, so if I forget some....sorry!
Magic Kingdom:
Adventureland: Swiss Family Treehouse
Frontierland: Tom Sawyer Island and the play area under the train tracks right next to the Splash Mountian entrance
Fantasyland: They just built a new Pooh area to play in, I havn't been there yet, but I will be in a month

They also have fairytail garden where Ariel sits for autographs...there is a water splash area there.
Toontown: Donalds Boat and right next to there is a fun play area for the little ones.
MGM:
Honey I shrunk the kids playground
Epcot:
Mission Space-In the exit of the ride is a play area for little ones (this is inside past the gift shop)
There is a couple playgrounds to play at around the world showcase and also a viking ship to play on in Norway
You also have the fun interactive areas in the Imagination building and also in Innoventions
Animal Kingdom:
Dinoland has the boneyard to play in or over at the Fossil fun games
Rafikis planet watch: Petting yard
I'm sure there are more that I'm forgeting about, I'm sure you will find plenty of areas to hang out and chill for awhile. I visited many of these last year with my 9 month old, since his brothers were busy on all the rides with their dad
