Bath - roman baths and what not
Manchester - brilliant shopping, nice place, original stuff... LOADS to do
Brighton - again shopping, but also the pier and lots of movie scenes
Oxford - lovely big city with great architecture, loads of beautiful things etc
Cambridge - really beautiful, everyone cycles...
Plymouth - lots of cool things

Sheffield - quite a different (and hilly!) city with nice architecture
Blackpool - blackpool tower...
Carlisle - see hadrian's wall
Dover - whiteee cliffs of doooooovaaaa
oh and COLCHESTER - britain's oldest recorded town with a big castle and meeeeeeeeeeeeeeeeee
i'd say the top ones (IMO and in order, if i were a tourist) are:
manchester, brighton, bath, oxford, cambridge... etc!