Scattered throughout the Toy Story in Space Play Set are chests that can only be opened by a specific character, here are the locations for all nine of those chests.
Beyond the "Costume" reward from the chests the selection is not specific to a character, what you get next in a chest depends on what you've already got.
Buzz Lightyear Costume
There is also a special Vault that requires all three of the Toy Story characters to unlock.
Toy Story Toy Box
After finding the set reward the remaining chests will give you a randomly chosen item from this list:
Infinity and Beyond
Pink Toy Story Horse
Toy Story Zebra
Blasting Zurgbot Enemy Pack
Zurgbot Enemy Pack