There's a shuttle to take his wife between the two hospitals, but not to take him between the east side and Columbia's Morningside Heights campus (which is 50 blocks from the hospital in Washington Heights where the shuttle goes).

For his wife, living at 70th/York vs. Washington Heights would make no difference, since she'd have to take the shuttle to get from one place to the other anyway. But for him, it would be much easier to get to Columbia's Morningside campus from Washington Heights than from 70th/York. It's not terrible getting there from 70th/York, just a bit more of a pain.

As for other considerations, 70th/York is definitely a nicer neighborhood than the vast majority of Washington Heights and is closer to places the OP might want to go to eat/drink/otherwise have fun. But it's not exactly in the middle of anything. The immediate neighborhood is completely dominated by the hospitals and boring high-rise housing and generic delis serving the hospital community. And the subway is accessible, but not exactly right there, either.