There will be nothing directly in the AppData folder.
Saves will be in a subfolder of one of the subfolders of one of the subfolders of the AppData folder. For example,
C:\Users\your-username\AppData\Local\publisher or developer name\game name
C:\Users\your-username\AppData\LocalLow\publisher or developer name\game name
C:\Users\your-username\AppData\Roaming\publisher or developer name\game name
As Mad says, another possible location is a subfolder of the Saved Games folder in your user folder
C:\Users\your-username\Saved Games\publisher or developer name\game name
There are other locations too. For example
C:\Users\yourname\AppData\Local\VirtualStore\Program Files\...
which is in the AppData folder but game and developer name are buried deeper than the Local, LocalLow, or Roaming folders.
You'll also find some game saves under the name of the game engine instead of the publisher or developer.
Sometimes you can figure out where they're located with a Windows search by date and time. Make a save, exit the game, and do a search for new or changed files to see if you can figure it out.
Very rarely you'll find something in your users Documents folder. I have saves from Puzzle Agent in a Telltale Games folder in C:\Users\username\Documents\Telltale Games\Puzzle Agent
but that was from an earlier version of the game than the current one.
It makes me nostalgic for the days of Windows 95/98 when saves would almost always be in the game folder.
Hopefully the link Marian found will help somewhat. At one point I found a list of all the possible save game locations, but I'm not finding it now.
acebook
witter
