Hayao Miyazaki is likely the most famous Japanese director in the world now that Akira Kurosawa (Ran) has passed on. Miyazaki is, of course, a director of anime films, the most famous of which are probably Spirited Away and Princess Mononoke. He also did Castle in the Sky, which WrittenWyrdd mentioned in a comment recently as an example of Steampunk. I find the visuals of Castle in the Sky completely amazing, but for me the story wasn't quite as amazing as the look.
Perhaps my favorite Miyazaki film might be one of his simplest - Kiki's Delivery service, the story of a young witch of 13 who goes off to find a town of her own. It's simple, but I like it from start to finish. Here is a clip on YouTube about 15 minutes in when Kiki is arriving for the first time at her new town. This link is in Japanese with subtitles, but you can find the movie in most any Blockbuster I would think with a new English dub done by Disney. I recommend taking a look here and then going to rent.