Delcamp.net has lots of free classical guitar scores of all levels. You have to register first (free) and after that you've got access to hundreds of pieces.
Your post mentions "simple" pieces but Asturias is right at the other end of the scale - They don't get much more challenging than that. As a general rule, if a piece is difficult to play, it's difficult to read too. I'd suggest pieces such as:
Bourree in Em by Bach or some etudes by Sor, Carulli or Carcassi.
And don't forget my notation reading lesson under Member's lessons >Fretsource's lessions. It also contains a "note reading trainer" for identifying notes wherever they appear on the staff.