Pick the Right Place
Before a single slab of concrete is poured, before one sustainably harvested two-by-four is set into place, somebody has to decide where to put the new hospital. This is true of any building, of course, but we're talking hospitals today.
You want to start with the doctor's creed: First, do no harm. That means don't put your big building in the middle of the wetlands, or on top of an old chemical dump, or even on perfectly good farm land that could be used to grow organic soy beans.
If there are old buildings in the way, like, say, a neighborhood, don't demolish it. That's beyond rude. Brigham and Women's Hospital in Boston moved all the houses in the way of its new construction to a new site -- intact. If you can't do that, have a deconstruction company come in and salvage what they can reuse, like flooring or brickwork.