Hi - we have just moved to SE from Manchester area (CHeshire/Derbys Border) - would move back tomorrow! - Manchester was our big city for shopping/culture/events/sports etc.
Grew up in Norwich, its a fabulous city, good choice of schools, but 6th forms a bit of a nightmare re competition so do your research. Also lived in Sheffield ( great city, lots to do, wonderful countryside, friendly, good property and schools) and Newcastle - would also happily return there tomorrow, as others have posted, it has got the lot, coast, great schools and shopping, 2 hours up the road to Scotland, the amazing Northumbrian beaches, etc,. Very strong identity and very much its own place.
Norwich is a busy, interesting city, nearish the coast, has its own identity, lots going on - there is another thread on here about places to live around Norwich, so that might help you decide, guess it depends on how far north you want to be and how old your kids are re schools etc.