An interesting question, indeed, and the Office applications are not all the same.
For the record, the Access equivalent of ActiveDocument (or ActiveWorkbook) .Fullname is CurrentDb.Name but that may not help you much. Also for the record the Word default is changed via Tools > Options > File Locations rather than Tools > Options > General as in Excel and Access.
The default location in Word (and, I think, Excel) is application-wide and accessible, and changeable, in various ways, none of them (to me) very intuitive. The stored (in the registry) default is also not necessarily the same as the current session default. If you open your document via the Open Dialog the default location for the current session is changed to match the document; if you open a document any other way it isn't. But you can only have one default location no matter how many documents you have open, so the best course of action really depends on exactly what you want to do and in which application and it certainly involves code.
Enjoy,
Tony