There are many reasons that I think a hospital on a hill is a bad idea. Here are my top 5:
1) Sick people don't have the strength to climb hills
2) Parking
3) Ambulances are not the best vehicles to speed up winding steep roads
4) Earthquakes + Gravity
5) When the fog settles around the hill, and a patient unfortunately has end-stage disease, they may look out their window and have a terrible existential moment. Am I already in Heaven? Is Hell this hospital room where I have to see the same residents everyday, much like Sartre's play No Exit? No joke, the following is a picture from the hospital on a hill.

--By Farrah, who is now giving bonus points to non-hill hospitals when comparing her residency choices