When Stykz is launched for the first time, it automatically creates a folder called "Animations" in the Documents (or "My Documents") folder under your user name. Whenever you choose File > Save (or File > Save As...) on an unsaved Stykz document, Stykz will display the Save As dialog and it will default to saving in the Animations folder. You may choose to save your document there, or you can navigate to some other location.
If you decide to "Save As" with a Stykz document that had previously been saved, the Save As dialog will by default point to the location where the original version of the document was saved. So for example, if you were to double-click on a .stykz file on your Desktop, launch Stykz, and then choose File > Save As..., the directory initially shown in the dialog box will be on the Desktop.