Tolkien's got women other than Éowyn, though you might not be able to tell that from the fans. What about Galadriel and Arwen?
Galadriel has that tremendous scene with Frodo where he offers her the Ring and we get a glimpse of how terrible and awe-inspiring she is -- and then she passes the test. She refuses the Ring and allows herself to diminish and ultimately disappear from Middle-earth along with all she rules.
And Arwen is a much bigger character than just in Lord of the Rings. Check out the appendices and the other related material. The sacrifice she makes for Aragorn is a tremendous one, and says a lot about her strength.
The movie doesn't factor into this. I couldn't think of anything Liv Tyler had been in prior to "The Fellowship of the Ring," and finally had to check on imdb.com to find out. Cate Blanchett I saw in Elizabeth, which barely gave her a chance to show her acting talent because the director did such a hackneyed job on the film that it was fairly incomprehensible.
One of the things that keyed my interest in the movie is that Peter Jackson avoided casting any "stars." Elijah Wood, Sir Ian McKellan, Viggo Mortensen and the others are all fairly well-known, but they don't have the star drawing power of someone like Brad Pitt, Michelle Pfeiffer or the others. I can name only one or two movies for several of the stars, and even fewer for none.
I like the characters for their own sake, which is why I would have been annoyed if they had cast Sandra Bullock or Jennifer Lopez as one of the elves -- it would have been an obvious attempt to cash in on someone's star status at the expense of faithful casting.