First off I need to declare a slight bias in my answer. I run a company that sells craft beer and real ale (24 Beers). So I think you can guess my answer; beer seriously represents around here.
To qualify that answer you only need to visit some of the local breweries. I live just outside Norwich on the beautiful Broads and just across the water from me you have Woodforde's. You need to try their Nelson's Revenge. Another of my favourite breweries is Humpty Dumpty in Reedham. There are so many really good breweries outside Norwich - too many to mention.
Within the city it gets even better. There's Redwell Brewery who have just started brewing the city's first lager in 30 years - which is pretty tasty. As well as fantastic breweries the pubs are cracking too. Coach and Horses on Thorpe Road and the Fat Cat have their own microbreweries out the back; Murderers (don't be put off by the name), The Plough, Plasterer's Arms and the King's Head.
There's the real ale trail around the city; right now is the City of Ale, a city-wide 10 day celebration of beer; every year there's the Norwich Beer Festival. And this year Norwich hosted the CAMRA (Campaign for Real Ale) AGM. So a fair bit going on.
Oh, we have whiskey too. The English Whisky Co. have recently released their own English whisky. But it's all about the beer for me.