The university is about 1.5 miles from the city centre, or 0-1 miles from most of the student housing areas. The hospital is about a mile further on.
The campus grounds are exceptional, look at an aerial map/photo of it and you can see the extensive grass areas and woodland, plus a lake and so on. The buildings are densely packed together in the middle and are the usual ugly concrete style, but it's fine really. Norwich city is renowned for its historic architecture and many surviving mediaeval buildings, so it's a nice city centre if you're into that sort of thing.