According to Twilighters Italia & Lion Lamb:
New Moon will not be shot in Volterra but in Montepulciano
Despite advertisements, anticipations and every kind of proposal from the major and the township, New Moon will be shot in Montepulciano because the locations are "more beautiful for the movie" than Volterra."
And, they were nice enough to post pictures of possible locations in Montepulciano. Although the movie may not be filmed in Volterra, these locations look accurate to the descriptions in the book.