In the Death Location field, you should list the actual place of death, not place of residence. I would list the town where the hospital is located, but not the hospital name, and list town, county, state, country. In the biography, I would list the name of the hospital so you have complete information.
I do not list the town where he was living, because that could be very different. I've had relatives who died while on vacation or visiting someone in another state - listing their hometown would throw me off the trail of locating a death certificate. Also, most of my relatives were from small villages and had to go to hospitals in another town, and the nearest hospital might be only a few miles away, but in another county.