The Tale of The Princess Kaguya, the latest from Studio Ghibli, doesn't have a major presence behind it. The film is slated for its LA debut this week, but as this is written has no link to get tickets and its official site is Facebook. It's supposedly going to be playing at the ArcLight Hollywood. Will update you if and when tickets become available.
The film features the voices of Chloë Grace Moretz, James Caan, Mary Steenburgen,
Darren Criss, Lucy Liu, George Segal, James Marsden, Beau Bridges,
Oliver Platt, John Cho, and Dean Cain. It recently won the Audience Award at 2014 Fantastic Fest.