There is no such directory;
%APPDATA% is Windows-specific. You'll have to abstract it yourself: create your own
GetSaveGameDirectory function that returns an appropriate path on whatever operating system you're running on. You can typically make this determination at compile time with preprocessor checks against the appropriate macros in C (and it's ilk). I'm not entirely sure of the best way to do so in Java.
On Windows, an
%APPDATA% subdirectory for your company or game is appropriate. On the Mac,
~/Library/Application Support/Your Game is common although Apple's guidelines recommend against storing "user data" there (it should go to the
~/Documents directory) -- it depends primarily on whether or not you prompt the user to select a directory).
On general *nix systems you'll probably find less standardization -- perhaps a hidden directory within
~, such as
~/.yourgame? Certainly this is the common practice for configuration files. An actual *nix user will probably need to chime in on whether or not this an appropriate game save location.
For the best results, do not hardcode the path to the directory based on the English string, but use the OS API to access the directory. This will help ensure your game runs properly on non-English version of the OS. For example, on Windows, use SHGetKnownFolderPath or an equivalent wrapper, if possible.