Get default image directory with styles large?
I'm not sure this will get you exactly what you want, but the 'default' path is just public://, so.

$url = image_style_url('large', 'public://');


will return

http://yoursite.com/sites/default/files/styles/large/public


I think it's more likely you're looking for a specific path, e.g.

$url = image_style_url('large', 'public://field/image');


which returns

http://yoursite.com/sites/default/files/styles/large/public/field/image