The Princess Diaries is a great little family movie (I think it holds up so well!) and in my opinion Anne Hathway was perfectly cast.
If you look at imbd trivia there is a looooong list of actresses who were allegedly considered for the part, but I don't believe a lot of them (like a 27 year old Juliette Lewis being offered and turning down the movie...). I do believe these three below because a producer of the film specifically named them as actresses who auditoned.
Would you have preferred any of them over Anne, ONTD?
(All pictures from roughly 2000 which is around when the movie would have filmed)