York is a great little place for a weekend break. It's a compact old city that has everything, Roman and Viking remains, a Cathedral, intact city walls, river excursions and some great museums.
The Shambles is one of the best preserved medieval areas in the UK with interesting narrow streets lined with half timbered buildings.
York Minster, the Cathedral (picture), is an impressive building dating mainly from the 13th and 14th centuries and is built in the early English Gothic style. It is the second highest ranked cathedral in the country and the seat of the Archbishop of York.
In 1984 a fire destroyed much of the cathedral but quick thinking actions by the fire brigade saw them deliberately collapsing the roof which saved the rest from certain destruction. The building today shows no effects from that devastating fire.
The only downside to York is the sheer number of visitors the city receives. It's a fairly small city center and it can feel oppressive with the volume of people, particularly on a hot summer weekend when the city is full of stag night and hen night party goers as well as the influx of tourists.
In terms of gaining a full WHS listing, I'm not so sure, it's a great place for a break but not on the same level as, say, Bath or Edinburgh