There are a wide variety of housing arrangements surrounding Yale New Haven Hospital. You can live right next to the hospital in Crown Towers or Crown Court or Madison Towers. I would also check out University Properties for slightly more expensive, but really nice places that are downtown. If you are the house/neighborhood type person...look in East Rock, otherwise affectionately known as the grad ghetto--though it is far, far from a ghetto. Lots of houses, little cafes, and it's close to the park and running trails. All fairly reasonably priced. Good luck.