It is important to not simply look, but also take mental notes. Many famous works can leave you cold, while some "lesser" work can move you profoundly. Just watching and soaking quality visuals might be beneficial, but it is really the analytical eye that leads to fastest progress. You probably know this, but two of the filmmakers you mention as inspiration have started their careers as film critics, which only reiterates the positives of the analytical approach.
As pointed by Mikhail, investing some time in paintings can be helpful. Classics are a great source of excellent compositions and will help tremenedously in developing an educated taste for composition and honing your compositional skills. Paintings can also further your understanding of light, especially some of the Dutch masters (most notably Vermeer, even though Rembrandt gets more love). And just walking around and paying attention to light and its behavior is a good excercise in itself: watch the quality and color of shadows, bounced light, reflections, highlights, modeling of shapes and lines, suggestion of form.
As you said that you are into film, you may delve into the work of not just directors but also some of the great cinematographers. I am a naturalist by heart, so I find the imagery of Roger Deakins, Emmanuel Lubezki or Chris Doyle very appealing. The work of James Wong Howe, John Alton or Urusevsky, for example, will demonstrate some excellent use of black and white. But, really, any film you like a lot visually you can rewatch with cinematography in mind. (I find that turning the sound off can help in appreciating the image for what it is.)
Once you have a sufficient base to build upon, judging the work you see and registering anything you happen to like can get you far. Jordan Cronenweth (who shot the visual masterpiece Blade Runner for Ridley Scott) once said that he steals every good idea he stumbles upon while watching other people's movies. This applies on many levels, because (post)modern art is highly referential and quotational. This is especially true in pop-culture but also applies to high art. And the broader your inserests, the more intellectual and emotional stimuli you subject yourself to - the bigger your database of memes and, hence, of possibly interesting associations you can offer to your audience.