Where does save( , '') save to?

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It saves to your current location, or "present working directory".

You can find this location with the command "pwd".

For example, if my username is "user" and I am working in a folder called "myproject", I might get:

sage: pwd
/home/user/myproject/

This directory us usually the place you launched Sage from.

Additionally, at least for certain types of objects, such as graphic animations, you can do

sage: a.save('filename', show_path=True)

so that the full path to the saved file is shown when saving the object to a file.