I wish I had more knowledge of northern cities, I keep meaning to remedy that, but haven't seen enough of the north of England to give an informed choice but Halifax, Harrogate (not sure if they're cities I thought were lovely when I visited.
St David's in Wales, is I believe the smallest city in Britain, and lovely with it.
Winchester, steeped in history, beautiful surrounding countryside.
My obvious best ones would be London, Bath and York, but we're not doing those, so I'll go with the three I've mentioned first.