Shopping:
Norwich has one of the best covered markets in the country, which is amazingly cheap. (50p for a cup of tea, for example, or a fiver for a good-quality leather wallet).
There are also two big indoor shopping malls (Castle Mall and Chapelfield) right in the city centre, where you can spend lots of money. A walk along Magdalen Street, though, will take you to the 'cheapo' end of the city, where you'll find lots of 'discount stores' and plenty of charity shops.
The city centre generally seems to be thriving, with very few empty shops (unlike many other towns and cities).
Culture:
Norwich has three excellent theatres (the Theatre Royal, the Playhouse Theatre and the Maddermarket Theatre), together with loads of other centres for the performing arts. Norwich is a city where you can find something different to see every evening.
Pubs, restaurants, etc:
There's something for everyone. (The wonderful, if rather pricey, Belgian Monk has already been mentioned. Real ale fans should try the Kings Head on Magdalen Street).
Crime, etc:
Norwich has one of the lowest crime levels, for a city of its size, in the whole of the country. As with any fairly large city, there are a few 'rough' areas but overall it's a safe place to live.
Friendliness:
East Anglian people aren't as naturally friendly as many northerners (for example). It's often said that you need to live in a house for at least 20 years before the neighbours stop thinking of you as a stranger. However, despite that, it's probably far easier to get to know the locals than in, say, London (especially if you drink in the King's Head!).
The area:
Norwich is a good base for exploring. The beautiful North Norfolk coast is within easy reach and it's only a short hop on the train to places like Ipswich (which is also blossoming into a really nice place these days) and Cambridge.
House prices/rents:
Generally far, far cheaper than London and the South-East but still quite a bit higher than in much of northern England.