I need to edit the way a default widget is displayed...where exactly are the widget files in the FTP space? I can't seem to find anything beyond a widgets.php file, but that's not it (not talking about the CSS, but the actual source code for the widgets themselves)
Try to be more exact what are you trying to edit. wp-includes/widgets.php is only file related to widgets.
how exactly are you trying to alter them? register_sidebar allows for some modification and its usually called in template/functions.php .