Florida Hospital - Orlando (the largest hospital in the U.S. by bed count and revenue) has been doing a lot in recent years to address this concern. They started by making the largest soda you could buy a 16oz (bottled or fountain), and have slowly phased out some food groups (such as fried foods) and have introduced entire cafeterias that only serve fresh vegetarian dishes. They have brought in community coffee shops that only serve fair trade coffee, and are working on setting up a food court type area that will house local restaurants that serve only healthy foods.
Florida Hospital Orlando is the Flagship hospital for Adventist Health, which operates 46 hospitals in the US and 26 hospitals/67 clinics in another 21 countries. It is a model that is being scaled to this other institutions.
FH Orlando isn't a hospital that is known for it's innovative care like the Mayo Clinic or MassGen, but it's size makes it a model for operations that these leading institutions follow.