Neither Amherst nor Columbia are particularly known for their physics departments but Columbia’s is likely better because, as you mentioned, it’s in the heart of NYC with access to the best of the best. Not to mention it’s an Ivy League so I’m sure there are some highly awarded physicists teaching classes. As for film, again Columbia shines - besides LA, NYC is the place for aspiring movie-makers to live, and though I’m not familiar with Columbia’s program specifically I’m sure it’s amazing.
And I’m saying this as someone who loves Amherst and doesn’t like Columbia. I’m completely with you about the core curriculum, it’s a huge con in my eyes. But at the end of the day, I think Columbia is the best fit.