Applications store their data in any or all of the following locations:
~/<individual application folders>
~/Documents/<individual application folders>
~/Library/<individual application folders>
~/Library/Caches/*/<individual application folders>
~/Library/Preferences/*/<individual application folders>
~/Library/Application\ Support/<individual application folders>
/Library/<individual application folders>
/Library/Caches/*/<individual application folders>
/Library/Preferences/*/<individual application folders>
/Library/Application\ Support/<individual application folders>
/private/tmp/<esoterically named folders>
/private/var/tmp/*/<esoterically named folders>
/private/var/db/receipts/
Also, it is not unheard of for an application to store data within its own application folder structure.
Please note that Time Machine does not backup everything. It will automatically exclude such things as iOS device backups among other items such as caches, logs, and what's in the Trash. You can view what is excluded by Time Machine automatically with this command:
cat /System/Library/CoreServices/backupd.bundle/Contents/Resources/StdExclusions.plist