If it's lively you're after, I would go for Manchester as first choice - it's certainly on the 'A' list when it comes to bands and nightclubs, and it has really good transport links to the rest of the UK and to Europe, for cheap travelling.
UEA is at Norwich, which is one of those underrated small cities that people don't think of when going through the standard list of cities. It's a characterful place and I'm sure the nightlife would be good, but I'd put it below Manchester mainly because your travel would be slightly hindered by the paucity of good transport, and because it would certainly be a notch lower in the high profile nightlife stakes.
Canterbury is a nice town, but is certainly the quietest of the three.