We spent a few days in June near Wroxham (very close to Norwich). Our best dinner was at a great pub called The Recruiting Sergeant. It's in Horstead, right down the road from Wroxham. The portions were very large and very delicious. The menu was huge and the bill was not. :-) I'd book ahead as the place was very full and looked like the local favorite.
My absolute favorite Norwich restaurant is a little hole in the wall place for fish and chips. When I was at UEA we went to The Chip Shop (I think it was 26 Stafford St.) every Thursday for fish and chips. We'd take our food down a few blocks to a small courtyard (I think it was for a rec center) and after we were finished, we'd walk around the corner to a bakery for apple turnovers. I'm sorry I can't be more specific about the location...it's been about 5 years since I lived there. I do remember that the shop was in the middle of a residential neighborhood. All I can say is that if you find this place you will be richly rewarded. The chips, doused in malt vinegar, were superb, and the fish was incredible.
I was partial to The Waffle House's garlic mushroom waffle. And their dessert waffle - fresh banana with chocolate sauce and toasted nuts - was to die for. http://www.wafflehouse.co.uk/
Logan's (5 Swan Lane, downtown) has really good sandwiches. I especially enjoyed the roast turkey with cucumber, tomato, mayo, salt and pepper on a crusty roll.
There is also an excellent Thai restaurant - Siam Bangkok - at 8 Orford Hill near a movie theater.
There was always a market downtown, in the town center. I only bought flowers from there so I can't speak to the food, but it looked good.