What city has a great city centre and possibly worth a visit (in response to the other thread about the worst city centres), but towns included too.
Edinburgh obviously, Carlisle is being spruced up and has a cathedral (it became a cathedral in 1133, many restorations but last was in 19thC)), smallish museum and art gallery, a castle and the station all within a short walk of the centre. The centre has lost quite a few of the usual shopping venues but still has a large M&S.
Beverley still has a nice old market town feel. The minster is impressive and St Mary's Church is lovely. One or two nice clothes shops.
Any other suggestions?