New Haven has good pizza, but not Yale.
It seemed to me cars were less necessary in Pasadena than they were 20 years ago when I lived there. Lake Avenue shopping is an easy walk from the Caltech campus. But I agree LA is a lot more fun with a car - especially if you want to take advantage of the beach, the mountains and the desert parks and the great museums. (Which we did.)
I agree Yale, sounds like a more likely fit, but there has to be some reason this student applied to Caltech.